Whether there was a historical nation called Palestine (anytime from circa 1000 BC to to early 20th Century). Partly, this swings on whether one should read sketchy ancient records of Philistines/Palistina/Walistina/Falistina/Palastin as identical with Palestine or not (as well as whether they indicate a country or an ethnicity, whether the concept of nationhood was historically comparable, etc., etc.). From the article at Wikipedia (footnote citations in the link):

Pro

Due to the similarity between Palistin and Philistines, Hittitologist John David Hawkins (who translated the Aleppo inscriptions) hypothesizes a connection between the Syro-Hittite Palistin and the Philistines, as do archaeologists Benjamin Sass and Kay Kohlmeyer. Gershon Galil suggests that King David halted the Arameans' expansion into the Land of Israel on account of his alliance with the southern Philistine kings, as well as with Toi, king of Ḥamath, who is identified with Tai(ta) II, king of Palistin (the northern Sea Peoples).

Contra

However, the relation between Palistin and the Philistines is much debated. Israeli professor Itamar Singer notes that there is nothing (besides the name) in the recently discovered archaeology that indicates an Aegean origin to Palistin; most of the discoveries at the Palistin capital Tell Tayinat indicate a Neo-Hittite state, including the names of the kings of Palistin. Singer proposes (based on archaeological finds) that a branch of the Philistines settled in Tell Tayinat and were replaced or assimilated by a new Luwian population who took the Palistin name.

Arguably this is archaeology, not history. Moreover, this example (like many other answers) is an ongoing politically hot issue, for which reason you may not want to introduce it to 12-year-olds.

OK, I'm not a historian, but I like history. How about the origin of the Sphinx? I think some of the recent theories (e.g. Colin Reader https://www.dailygrail.com/2014/06/did-the-great-sphinx-of-egypt-originally-have-a-different-head/) make a lot of sense, but the the traditional Egyptologists reject his ideas.

If you're looking for something where the evidence is undisputed, but the interpretation varies, a good choice would be the starting date of World War II. The three mainstream dates:

• July 7, 1937, with the start of the Second Sino-Japanese War.
• September 1, 1939, with the Invasion of Poland.
• December 7, 1941, when the attacks on Pearl Harbor, the Philippines, Guam, Wake Island, Malaya, Hong Kong, and Thailand merged the European and Asian conflicts into a single world-spanning one.

Other, non-mainstream starting dates go back as far as July 28, 1914, with the idea that World War II was just a renewal of the fighting of World War I.

Might be somewhat controversial, and I believe older historical debates are safer grounds, but what about how much blame Hirohito deserves for Japan's entry into WW2? Two views exist:

• Hirohito, as per ancient Japanese imperial tradition, was a revered figurehead ruler. As such he was not expected to influence government policy directly, but rather serve as a unifying figure and perform national-religious rites.

• Hirohito was regularly briefed by the military, could have appealed to the nation through his moral prestige and, at best did nothing to stop the war, at worst was a proponent of it.

You can interpret entry into WW2 as you fit. Maybe it's Pearl Harbor in 1941, maybe it's Japan's aggressive policies in China from 1931 on. Either way, what was Hirohito's influence?

1. The classic question for this age group is the use of atomic weapons in the Pacific War. Was it necessary? Was it just? How does the ending compare with the foreign policy aims of the US prior to the raid on Pearl Harbor, and afterwards? To what degree were decisions made based on moral grounds, as opposed to the mere existence of the weapon driving its use.

2. You could also usefully debate the starting date of World War Two, as historians such as Max Hastings and John Keegan argue that the conflict should date from the Japanese invasion of China and that a later date is mere Eurocentrism. That's an interesting discussion about cultural bias and history.

3. If you feel the students don't have much knowledge of history then that's fine. Because your students have just lived through a notable era: Trump, BLM and Covid. What controversies will future historians see in those events? What materials would they seek to resolve those controversies? Are those primary materials being conserved now? And if not, are we seeing how history can be shaped by the availability of sources? Note that the trick here is to use the controversy as a lever into the issues of history, not to explore the controversy itself.

The recent era is also a useful reminder that anyone can be a historian: so much of modern life is now ephemeral that a collection of curated primary materials is gold. In Australia there's a person who has tweeted every Covid media conference by every official. The pandemic is only 1.5 years old and that's already a much-used resource. But even a curation of memes or tictoks of the past 1.5years has tremendous value to the future.

I think Jesus of Nazareth can be a proper candidate for this question. Quoting verbatim from Wikipedia:

There is widespread disagreement among scholars on the historicity of specific episodes described in the biblical accounts of Jesus, the details of the life of Jesus mentioned in the gospel narratives, and on the meaning of his teachings. Many scholars have questioned the authenticity and reliability of these sources, and few events mentioned in the gospels are universally accepted.

There are a lot of ongoing debates in this regard, including the date and place of birth. Another Wikipedia article is a good place to start:

Reconstructions of the historical Jesus are based on the Pauline epistles and the gospels, while several non-Biblical sources also bear witness to the historical existence of Jesus. Since the 18th century, three separate scholarly quests for the historical Jesus have taken place, each with distinct characteristics and developing new and different research criteria.

For what it's worth, I think you should flesh out some of your discussion on this topic with things that people were once bitterly divided about but which were later resolved in various ways. As you and om noted, the historicity of Troy (resolved in favor) alongside the Romans' Aeneid myths and England's legends on Brutus and the Matter of Britain (resolved very much against). You could follow that by issues where different historians made various judgment calls on either side of the Cold War, with the actual history only slowly trickling out and changing everything we thought we knew (eg, JFK facing down his own generals over the Cuban Missile Crisis and secretly accepting the removal of missiles from Turkey as the ultimate compromise while denying any concession in public).

As far as non-religious topics that remain unresolved but still interesting to 12-year-olds, aside from those already mentioned:

Are Japan's emperors—who have maintained a single dynasty for 2000+ years—the descendants of a Chinese refugee mystic? To make that sound a little less crazy, you can just talk about how historians are divided (especially between Chinese and Japanese academics) about what precisely happened to Xu Fu (徐福) when he fled the First Emperor's demands for an elixir of immortality into the eastern sea with 3000 young men and women and shortly thereafter Japanese agriculture and society began massive development.

If you want to keep things western and talk around the historicity of Jesus without ruining the rest of your year, there's the issue of How accurate was Plato's account of Socrates? There are very important points to be made to modern children about the way that Socrates—however much he's revered for his clarity of thought and humanism—was basically put to death by the Athenians over anger with his students' pro-Spartan despotism. People disagree strongly over whether he was simply an elitist or whether he felt democracy could work with the right sort of education... or whether we can trust what Plato wrote at all.

Did the Romans invade and hold Scotland for a period of years? Our sources are incredibly fragmentary and possibly self-serving, but archaeological discoveries keep pushing Roman activity further and further north even if they eventually decided that none of it was worth the expense of kitting out their legions, leading them to withdraw south.

War of 1812: USA regards it as preventing the UK from pressganging US sailors. The UK and Canada regard it as a US land grab for Canada.

Factors I'm using

• Preferably, it should be about some subject that they have already learned
• If possible, there should be only two big theories (and maybe a few alternatives with minority support), with the debate being mostly about which of them fits the available data better
• It shouldn't be too politicized (cuts off most of the "was X real?" options) and/or too focused on emotions (cuts off most of the "why X did Y?" options)
• Nevertheless, both theories should have fairly wide level of support; it shouldn't just be "one guy has a theory that disagrees with everyone else", so e.g. Marco Polo is out

With that in mind, here's my current proposals; I might add some more if I manage to think of any.
(I actually only had the first one [now second] until I almost finished writing it down and then suddenly thought of another [now third].)

EDIT: I've asked my brother (15 years old, passionate about history) and got an answer that I liked so much I'm putting it first. (I'm keeping the other two to avoid confusing the upvoters too much.)

Death of Alexander the Great

Alexander III of Macedon, aka Alexander the Great, conquered most of the then-known world before unexpectedly dying in 323 BC at age 32 (a month short of 33) in Babylon after about two weeks of illness.

People, especially rich people, didn't particularly often randomly die of natural causes in their 30s back then any more than they do now.
So did he die of an infection? Was he poisoned? Did he perhaps get a food poisoning or something? If it was a murder, then why, and how?
Historians debate these questions to this day.

Possible bonus inclusion: where he was buried, and what happened to his tomb? Its location is currently unknown, and legends abound.

Pros

• Alexander the Great was probably the most important person in the entirety of ancient history, and his sudden death was arguably the most important event in the entirety of ancient history
• The political implications of his death, to the extent that there are any, are for the most part about it having occurred at all, rather than the specific cause, so there aren't a lot of politically-motivated theories trying to prove a particular scenario
• Kids love murder mysteries ^{[citation needed]}

Cons

• To a large extent, the true answer is unknowable; there's just not that much evidence, especially regarding possible reasons to kill him
• 12-year-old children might be too young for an extended discussion about sickness and poison symptoms

The other two options (which I came up with by myself) are listed below.

Chronology of Mesopotamia: middle vs. short (and the other alternatives)

TL/DR: when those kids learned about Mesopotamian civilizations, they probably received some dates associated with them. Which dates? Were those dates correct? And how do we know?

This might be a bit too complicated (and/or too vague) for a "major historical event", but this is certainly a debate that historians are still uncertain of to this day, with evidence on both sides, despite sources.

The chronology of Mesopotamia is, to a large extent, floating; there's usually (though not always) enough evidence to say that event A happened X years after event B (there's a lot of those cuneiform tablets, and we're constantly finding even more), but there's not necessarily enough evidence to say that any particular event C (in the earlier areas, anyway) happened Y years before the common era.
There's a bunch of astronomical evidence (most notably the Venus tablets of Ammisaduqa) allowing historians to fix the options to only a few possibilities, and a bunch more extra evidence (e.g. radiocarbon, dendrochronology, inter-regional synchronisms) that can be interpreted to favor a particular side (though which side it favors can itself be disputed).

There are similar considerations in Egyptian chronology, but the situation for that is quite messed up (not helped in the least by the main source for it being in absolute tatters), whereas for Mesopotamia historians, for the most part, have a very good idea that is down to only a few possibilities.

Pros

• Limited to only two major options (plus some minority candidates, still not many - maybe four or five - outside the extreme fringe)
• Essentially civil; approximately nobody cares all that much about when exactly the events happened (except the fringe, which for the most part doesn't accept any of the mainstream options anyway), so there isn't much of a heated dispute
• The general subject of "how do we know when this happened", and even more generally "how do we know what we know about history", is very important to consider, especially if anyone in the class is thinking about becoming a historian

Cons

• Approximately nobody cares all that much about when exactly the events happened (and many of the people who do care don't like any of the mainstream options), so the dispute is of fairly low importance
• The evidence for or against the different chronologies, or possibly even the chronologies themselves, might be a little too arcane for 12-year-olds to understand
• There isn't really anything cool riding on it one way or another; it's just so much numbers

Was the Indus script (and/or the Easter Island script) a full writing system, or just some pictograms that weren't intended to be read as a language? Or even something in between?

Ever since the seals at Mohenjo-Daro (and/or the rongo-rongo tablets) were discovered, historians had debated whether they were, in fact, a real writing system for a real language, or just some generic pictograms (something like logos, desktop icons, or emoji, to take comparisons intelligible to 12-year-olds).

There's a bunch of evidence on both sides, but not all that much for either, and the civilizations in question are sufficiently far gone (and were sufficiently unconnected with other civilizations that historians do know more about) that there's not much non-internal evidence to be gained (outside a particularly lucky break).

So historians basically have to deal with what little evidence they do have - which results in some unexpected considerations.

Possible bonus inclusions: Phaistos disk, Voynich manuscript, quipu.

Pros

• Not just a bunch of numbers but something with actually interesting relevance
• The general subject of undeciphered scripts - in some cases (e.g. Linear A) we know that something is a script but don't know (much about) how it is supposed to be read; in some other cases (e.g. Etruscan) we know how it is read but not necessarily what it means
• You can also talk with your students about whether emoji count as a language, and/or ask them to imagine a bunch of signs written in emoji found by a future civilization

Cons

• The question invites a lot of kooky opinions (particularly of the spiritual variety), and there are so many of those that they start overshadowing the genuine opinions
• In the case of Indus script the question is also highly politicized, because the authorities of India really want people to believe that the Indus Valley civilization is a direct ancestor of later Indian culture
• The evidence favoring one interpretation over another probably won't be easy to explain to 12-year-olds (not that it's particularly easier to explain to serious historians)
• If your students hadn't heard of the Indus Valley civilization they might be lost at the very start (though they probably have at least heard of the huge heads from Easter Island)

Who first discovered America?

Common ‘wisdom’ in the US is that it was Christopher Columbus, and the public schools in the US generally say exactly nothing more.

Prior to that though, the Norse peoples colonized Greenland (around 980 CE), and there was a short-lived Norse colony established in what is now Newfoundland (specific people to look up are Leif Erikson, often quoted as having discovered North America before Columbus, and Bjami Herjólfson who actually discovered it before Leif).

From there, you get into more fringe ideas.

• There’s compelling but inconclusive evidence of Polynesian, Melanesian, and Austronesian contact on the Pacific coast.

• There are numerous claims of East Asian (mostly Chinese or Japanese) contact existing prior to this, including claims that Chinese refugees were responsible for the establishment of the Olmec civilization.

• Various other claims exist of pre-Columbian contact from various cultures, including India, Rome, various African cultures, Egypt, Arabs, Phoenicians, and (thoroughly debunked) Jews.

And of course, up until recently many people conveniently ignored that America was actually first discovered by Paleolithic hunter gatherers by crossing the Beringia land bridge at least 14 000 years ago (but probably more accurately at least 33 000 years ago based on evidence found in the past two decades).

This allows for exploring not only the type of debate you want, but also explaining the way that historical fringe theories develop and showcasing how cultural chauvinism can significantly impact acknowledgement of scientific discoveries, as well as the concept that ‘history is written by the victors’ (both contributing factors to the regular claims that Columbus discovered America).

I recently read that some years ago, some scholars formed the view that there never was an Catharic heresy, much less a Catharic religion, not even a separate Catharic "church" organisation. All that there (supposedly) was were some major misunderstandings within Christianity. E.g. that most of this article is mistaken. This might be a good example of how even major and well-documented events are still open to re-interpretation.

There are some events where the background or what actually happened is unclear and it seems like each author has his own opinion. E.g. the succession from Cambyses and ​Bardiya to Darius in the Persian empire. Another such example might be the reason for keeping the death of the 5th Dalai Lama secret for some decades (or whether it actually was kept secret). These are both a bit obscure, but might make a good story.

There has been discussion whether Marco Polo really went to China but I am not sure if this is seriously debated (rather than just refuted) among historians.

Re Troy, my impression is that there still is a serious debate about whether the site dug up by Schliemann is the Troy described by Homer. AFAIK it is accepted that the site dug up by Schliemann was already identified as Troy in classical antiquity (and visited e.g. by Xerxes and Augustus). But there is the distinct possibility that the people in classical antiquity were wrong, given that there were a number of centuries between the (supposed) Trojan war and the earliest recorded visits of "Troy". At least among German historians, there is still a reasonably controversial debate about whether Hisarlik = Homer's Troja.

Another very classic topic might be the reasons for the fall of the Roman Empire. Or, less sweeping, the relation between Xiongnu, Attilla's Huns, and the Hephtalites in Iran. All the same, all different, something in between?

The Kennedy assassination would seem a prime example of disputed history, as would the role of the Mafia in John Kennedy's election as President.

The Rosenberg trial would be another.

Whether the United States was properly informed of the Pearl Harbor attacks is still a question of some debate.

The Vela incident was a possible nuclear weapon test in the South Atlantic which may have been a test of an Israeli design with the cooperation of South Africa and with some complicity of the US, would be an example.

The Gulf of Tonkin incident is still widely questioned.

The Sacco & Vanzetti trials of the 1920's (1921-1927) might be a bit obscure today but was the cause célèbre of its day.

Looking at earlier times, the fate of the Two Princes in the Tower of London is still disputed.

Whether the Chinese or other groups made it to North America before the Vikings is still in question.

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Obviously, not to include Native American groups whose arrival is, itself, undergoing revision as to dates.

The link between the Celts and the peoples of Northern India is still undecided. Their mythologies line up tremendously well.

A fun one is, who should actually have won the 1972 Olympic gold medal in basketball. There were a number of irregularities involving the clock at the end of the game.

The stance of Pope Pius XII towards Nazi Germany has been in the news a lot recently.

Some ideas from the top of my head.

Did Marco Polo Really Go to China?

There are two major theories/groupings about Marco Polo's claims and publications that he travelled to China with his uncles and lived there for many years.

1. It really happened basically as he claimed, or
2. He actually was in Turkey, Persia or some other midpoint most of that time and his information about China was based on stories that he heard from Chinese merchants and visitors whom he met there and/or on historical documents that existed in Persia at that time.

This has been hotly debated literally for centuries and the scholarly consensus has flipped more than once (even within the last 20 years). You can see some of this here, and here. For a lot more fun, check out the "View History" tabs for the Wikipedia page (and also for the Wikipedia Talk page). This is the Debate section from the Wikipedia article c.2016 which I think demonstrates well the number of different scholarly articles both for and against the veracity of the stories. IMHO the only fair way to characterize this state of affairs is "very undecided".

The advantage of this topic is that the story of Marco Polo is something that almost all schoolchildren have heard of, though perhaps not the details and usually they are not aware of the controversy.

As noted in the comments much of the historiographicaly significant and legitimate criticisms and questions have been edited out of the Wikipedia article as the academic consensus has changed over time. Additionally, as an encyclopedic article, it is policy to edit articles down to representative summaries of the positions. If you check the histories of the article and the talk page, you will find more information on the controversies. Also, if you cast a wider net, such as this section from the article on Marco Polo's book itself hints at much of this. So be sure to look for other sources of (legitimate) information.

Troy

You can start with the Schliemann discovery, the so-called Priam's treasure, the realization that there were different layers, pinpointing Troy VII as probable Homeric Troy.

• Fits into the history they know.
• Unlikely to let modern passions hide the lesson you want to drive home.

Well it's a pity that the only civil war your class is aware of is a fictional one between superheroes, because otherwise the US civil war fits your criteria perfectly I think.

My personal opinion and the opinion of a lot of historians today is that the Confederacy fought to preserve the evil institution of slavery, however there were and still are a lot of historians who insist it was about "states rights". As an extra bonus this disagreement between historians was and is not just academical. It had a lot of real-life consequences in among others the Reconstruction era and the Civil Rights era. Even in the present day how the Confederacy and the people who fought for it should be judged causes political tensions sometimes.

How about the Late Bronze Age collapse?

It would fit nicely into the background you provided under point three and I think could be explained at an age-appropriate level with lots of somewhat commonly known examples.

The different theories (eg. the mysterious "sea peoples") should be quite exciting to discuss.

The Anglo-Saxon invasion/settlement of Britain?

It's agreed that in the space of a few centuries, most of Britain went from being:

1. mixed Christian/Pagan in religion
2. mostly Celtic-speaking by language
3. Romanized in culture

to:

1. Germanic Pagan in religion
2. mostly Germanic-speaking
3. Germanic by culture

But how this change took place—whether this was a mass settlement and takeover or an elite military takeover—is unclear and hotly debated.

On a lighter note (compared to the suggestions in other answers), possibly more suited to 12-year olds and with no possible covert political/religious/etc message, try:

• Did Robin Hood exist?
• Did King Arthur exist?