The war that started on July 7, 1937 was a "local" war in Asia, between Japan and China.

A second "local" war in Europe between Germany and Poland in Europe started September 1, 1939.

On September 3, 1939, Britain and France declared war on Germany for invading Poland on September 1, 1939. On September 17, 1939, the soviet Union invaded Poland. These events were close enough to September 1, 1939 for them to be to (retroactively) attributed to events of the earliest date.

By September 17, 1939, Britain, France, Germany, Poland, and the Soviet Union were all involved in the (European) war, plus the Empires of Britain and France. The two "Empires" included Canada, Australia, India, large parts of Africa, and parts of Southeast Asia, (Myamar, Malay, Indochina, etc.) "All of the above" represents enough of a "critical mass" to call the hostilities a world war.Among the major powers, only the United States and Italy were not involved in one war or the other.

Germany, Italy, and Japan signed the Tripartite Pact in 1940, which "retroactively" merged the two wars into one.

But the best answer is probably that September 1, 1939, represented the date of "no return" for a formerly peaceful world.

Isn't that just a matter of perspective?

I wonder what the Russian text books say is the start date?

There are so many good candidates!

• September 1st 1939: Germany invaded Poland
• September 17th 1939: Russia invaded Poland in partnership with Germany
• November 30th 1939: Russia invaded Finland (a disastrous war which helped convince Germany that the Russian army sucked)?
• June 22nd 1941: the day Germany invaded Russia

For Germany, it was definitely September 1st 1939.

For Italy, the war probably began on October 3rd 1935 when they invaded Ethiopia.

For America, the war began December 7th 1941.

For Britain (and France), the war began September 3rd 1939.

For China, July 7th 1937.

For Japan, it is less clear: they executed a series of creeping expansion all through the 1900s, until it all blew up in their faces.

I think what I am trying to say is, dates really aren't as important as high school history teachers make them out to be. Yes, you need to know the dates, but more importantly, we must understand how the EVENTS that took place on those dates affected each other and the world we all live in today.

Because, like it or not, all of us are living in the shadows of events that took place hundreds of years ago. I would say our politics, our culture, even our lives are shaped by those events.

As the World War II Article says:

Japan, which aimed to dominate Asia and the Pacific, was at war with China by 1937[5][b]—though neither side had declared war on the other. World war is generally said to have begun on 1 September 1939,[6] with the invasion of Poland by Germany and subsequent declarations on Germany by France and the United Kingdom.

So, formal declarations occurred at the later date, and gathered more directly attacking sides, enough to call it a "World War", where before it was China + Soviets + USA vs. Japan. Although, from @chepner's comment, that alliance did not involve formal war declarations:

The US did not declare war on anyone until December 1941. The USSR didn't declare war on Japan until August 1945.

From Second Sino-Japanese War, as of the 09:16, 16 October 2018‎ DimensionQualm revision... At the start of the second paragraph, it says the following:

China fought Japan with aid from the Soviet Union and the United States.

Although, even though that sentence is placed early in the page, it may be talking about events that occurred after the war merged with World War II.

As to why en.wikipedia lists particular start dates, I commend to you en.wikipedia’s arcane consensus policies, the article’s page history and talk page history. For why anglophone editors from the global north construe the texts they read to support their edit warring, I supply the following:

Popular conceptions of history reflect myth-making, national imaginations, language barriers and politics.

As the phrase “world war two” isn’t a technical or theoretical concept in history—compare to “imperialist wars” which is baggage laden—we should look to the reasons in popular history.

Firstly, the world system has concentrated imperialist power in “the global north.” Japan has a notorious unwillingness to tolerate public discourse on its war with China, this being viewed as a political issue related to which class ought to control the economy.

That leaves European powers and the anglophone settler states. These cultures are heavily Eurocentric. Britain and France in particular have large associated language communities—many of which are former colonies pulled into 1939—which emphasise 1939. Polish remembrance is obvious. German culture was specifically disciplined for 1939. Other states: Denmark, Norway, Netherlands, Belgium, Yugoslavia, Greece; were pulled into the 1939 war. The former Soviet Union memorialised anti Hitlerism and so also engaged in 1939 myth making.

China seems to be engaged in an exceptionalism connected to anti-Japanese anti-imperialism, and so doesn’t need “WWII” as a myth: the Sino-Japanese wars as the birth of the PRC suffices without needing a grand narrative of World War.

The US is slightly different, with a strong pull to 1941 for local reasons.

Centring social myth on 1939 reinforces the centrality of the global north’s Eurocentric myths, as essentially “the world.” The world naturally being France, Germany, the UK, their colonies and European victims. Given the decline of national imperialisms whose metropoles were European, 1945-1980, there are strong “dying empire” reasons to memorialise WWII on European terms: consider the UK’s war myths and imperial “decline.” Correspondingly the Great Patriotic War as an antifascist war in the Soviet Union was essential myth making, and the idea of a “popular front” against fascism harkens to 1939 for WWII. (The Soviet Union being transnational imperialism.)

Historians are unlikely to set a flag in the ground over sloppy nationalist posturing on a term which isn’t relevant. For long duration histories of world systems, that a period of war between metropole states existed 1914-1945 matters. At closer focuses who exactly was at war with whom matters more than a label.

It is a popular term whose meaning is political and no answer particularly interests historians. In fact, comparing why people support answers is more interesting than the idea of any particular start date.

Short Answer

The Wikipedia entry for World War II uses the start date of 1 September 1939 because Wiki is applying the Wikipedia definition of the term "world war" as a basis, for internal consistency. One must start with a definition of that term to formulate an answer as to why.

Long Answer

Many good answers here already - each with valid points to consider, and any one of which I could accept if I had posted the question (and a +1 from me on more than one of them). However, the definition of World War has not yet been addressed (i.e. when is it appropriate to use the term World War in connection with an international conflict?).

The various definitions of the term itself include no objective criteria (e.g. 60% of nations of the globe, or 60% of the land-mass of the globe, etc.) but rather subjective criteria. For example, if using Merriam-Webster's definition (my emphasis added):

a war engaged in by all or most of the principal nations of the world

... one must first decide what constitutes a principal nation, and then, if they are not all engaged in finding ways to kill each other, we move to the next qualifier, most, and then try to decide how many is "most"? 50.00001% or more? Does most require a two-thirds majority? Three-quarters?

With such subjective measures and no objective qualifications, one then turns to historical usage of the term to find a less subjective answer. Who first uses the term, and when? Are those sources considered authoritative?

From the Wikipedia entry on World War, there is much to be learned about the historical use of the term, which may provide an acceptable (if not definitive) answer to this question. It comes down to this: When does an international conflict become a World War? Definition from Wiki:

A world war is a large-scale war involving many of the countries of the world or many of the most powerful and populous ones. World wars span multiple countries on multiple continents, with battles fought in many theaters. While a variety of global conflicts have been subjectively deemed "world wars", such as the Cold War and the War on Terror, the term is widely and generally accepted only as it is retrospectively applied to two major international conflicts that occurred during the 20th century: World War I (1914–1918) and World War II (1939–1945).

Origin of the term (also from the same Wiki, my emphasis added below):

The Oxford English Dictionary cited the first known usage in the English language to a Scottish newspaper: the People's Journal in 1848: "A war among the great powers is now necessarily a world-war." The term "world war" had been used in 1850 by Karl Marx and his associate, Friedrich Engels, in The Class Struggles in France. Rasmus B. Anderson in 1889 described an episode in Teutonic mythology as a “world war” (Swedish: världskrig), justifying this description by a line in an Old Norse epic poem, "Völuspá: folcvig fyrst i heimi" ("The first great war in the world".) German writer August Wilhelm Otto Niemann had used the term "world war" in the title of his anti-British novel, Der Weltkrieg: Deutsche Träume (The World War: German Dreams) in 1904, published in English as The Coming Conquest of England.

In English, the term "First World War" had been used by Charles à Court Repington, as a title for his memoirs (published in 1920); he had noted his discussion on the matter with a Major Johnstone of Harvard University in his diary entry of September 10, 1918.

The term "World War I" was coined by Time magazine on page 28b of its June 12, 1939 issue. In the same article, on page 32, the term "World War II" was first used speculatively to describe the upcoming war. The first use for the actual war came in its issue of September 11, 1939. One week earlier, on September 4, the day after France and the United Kingdom declared war on Germany, the Danish newspaper Kristeligt Dagblad used the term on its front page, saying "The Second World War broke out yesterday at 11 a.m."

The Wiki section on Other global conflicts lists wars which, while global, have not been given the term "world war" (especially World War in capitals, which Merriam-Webster declares to be reserved for WWI and WWII, thus far in history anyway). Why were these other global conflicts not called World War X, Y or Z? Because no one did call them that. And no one does. Though anyone could. It is a socio-political term, not an objective or empirical one. It is a coined phrase. Those who coined it get to shape or influence how it is used. Like D-Day ... every operation prior to 6 June 1944 had a D-Day (day of commencing operations) and an H-Hour (starting hour). After June 6th, the term became synonymous with Operation Overlord and no one thinks of it in any other manner now.

In reading through the definitions and accepted use of the term, the consensus seems to be that there were global conflicts transpiring before 1 September 1939, but the tipping point to qualify it as a World War (among those who define or shape language or terminology, at least in a popular cultural sense) came when hostilities broke out 1 September 1939 when Germany invaded Poland, which, by treaty, resulted in war being declared by the UK and France (and their respective world-spanning empires, thanks sempaiscuba) on 3 September 1939. Why not use September 3rd then? Because technically a state of war existed upon Germany's invasion of Poland (by way of treaty) 1 September 1939.

As a parallel example of a technical state of war, refer to Roosevelt's Day of Infamy speech given to the US Congress 8 December 1941 (a day after the attack on Pearl Harbor) in which he said in conclusion of his remarks (my emphasis added):

I ask that the Congress declare that since the unprovoked and dastardly attack by Japan on Sunday, December 7, 1941, a state of war has existed between the United States and the Japanese Empire.

The US Congress declared war on Japan 8 December 1941, but that was a legal formality. A state of war existed upon the attack 7 December 1941 (and also by virtue of Japan's declaration of war on the US and UK 7 December, though delivered after the attack started - the attack itself started the state of war). This same logic can be applied to the state of war in Europe between Germany, Poland, the UK and France which commenced 1 September 1939 when hostilities began.

Those who coined the phrase "World War II" applied it to that war which started between those four nations and their global empires when Germany invaded Poland 1 September 1939. And it stuck. And it became accepted as such. It can also be rejected as such.

While Questions that ask "Why..." often invite opinions (and some good ones have been expressed here in some Answers and Comments), this Question can be addressed from a marginally historic perspective, and that is by examining the historical use of the term World War II, when it came into use and by whom, what are its roots in previous usage for other global conflicts (etc.) - hence why I chose to post this Answer from that standpoint. I think this approach can keep the Question grounded in terms that are not primarily opinion-based (even though use of the term may well be challenged as opinion- or politically-based) in hopes that by doing so this Question can remain open for years to come with many more great Answers and Comments added (which at some future date others may refer back to for historical perspective by the way) without fear of having this closed for being opinion-based.

Because it was the participation of the British and French empires, beginning with Declarations of War against Germany on Sept. 3, 1939, that turned several isolated regional conflicts into a World War.

The other conflicts of the 1930's had either already substantially ceased (as the Italo-Ethiopian and Spanish Civil wars) or been strictly regional affairs as in the Sino-Japanese War.

Because of the u-boat warfare between Germany and the British Empire, the conflict that started in Poland was immediately being fought on (and under) the seas of the North and South Atlantic as well as in Central and Western Europe. Additionally Commonwealth troops from as far away as Canada, Newfoundland, South Africa, Australia and New Zealand were mobilized into theatres stretching from the British Isles to the Middle East, and then India and the Pacific.