One internal dynamic is both unique to revolutions and maybe the single most powerful reason behind "eat their own" -- I'll refer to it as Bad Karama in its simplest "you reap what you saw" form.

Taking on the system, on the establishment, could be a messy and risky business. Revolutionaries often start from a precarious position, they have to keep the momentum going at all costs -- and that's just one of many reasons the rebels must act with significantly relaxed moral rules. Feeling anxious and stressed on both sides doesn't help; fear is the root of all evils, it makes us dumb and makes cruel.

Worse still, many revolutionaries actually glad they can drop the pretense and "make them pay" for real or perceived transgressions -- that would put them firmly in the wrong.

In effect, revolutionaries might effectively lose their right to appeal against unfair treatment and any other protection that a high moral ground would offer.

Bur the most serious issue could be our ignorance about the way Karama works. Most know about the Golden Rule. What they don't realize is that the Golden Rule is just the tip of the iceberg. The most damaging aspect of Karama is always instant and just as inevitable -- and it comes in the form of our relationship with ourselves. The latter is governed by the same rules as our relationships with others. We treat ourselves the same way we treat everyone else (tho special attention should be paid to those we don't particularly like or our enemies -- because we are often the worst one).

People doing evil punish themselves.

That's why we should be careful not to judge people -- we will end up judging ourselves just as harsh. The other way works as well. Many find it hard to love themselves for that reason. The right way to do it is to realize that:

1. For starters, when they say self-love, they really mean self-compassion, and
2. Focus, again, should be on the other -- of we can manage to develop compassion for others, self-compassion would follow automatically.
3. Compassion, as love in general, is understanding before anything else (if there even is anything else).

There are many excellent answers here which I have upvoted. (I'll add that I particularly like the point that revolutionaries are people who like us all are tempted by power which they are loath to surrender.)

But to those answers I'd like to add a point about violent ideological revolutions. (The American Revolution, like the Glorious Revolution, was not outsiders overthrowing an ideology, but insiders preserving one. A different kind of beast entirely. Some of the revolutions after the Fall of the Soviet Union were more a case of moving into a power vacuum than of violent overthrow of the established order. I'm speaking of neither of these sorts of revolution.)

The types of people who conduct an ideological revolution are themselves the major cause of the circular firing squads. No one carries a violent ideological revolution very far without far above average levels of chutzpah, zeal, self-confidence, intellectual arrogance, you-name-it. This overwhelming belief must be great enough that you're willing to destroy people and societies for the sake of things inside your own head.

Such is not the sort of person who deals well with diverse opinions: People who think differently are the enemy; the rare people who think the same are rivals. In the end there can be only one...

Marxism is most notorious for 'eating their own" First they cultivate a mindset of revolutionary reaction to perceived or real tyranny Then they kill that generation; so they cant do it again. Venezuelan history in a nutshell.

• 1992: They were the 3rd richest country in the Western Hemisphere behind US and Canada
• 2001: Voted a marxist president to address income inequality
• 2004: Healthcare completely socialized to public fanfare
• 2007: All higher education becomes FREE fanfare
• 2009: Private firearm ownership is banned
• 2014: Opposition leaders are imprisoned
• 2016: Food shortages become widespread, news reports of consumption of dogs, trash, and zoo animals become widespread
• 2017: Constitution/elections suspended
• 2019: Venezuelans massacred by government, Civil war begins In no more than a generation

In these kinds of situations, the divide is between the call for "continuing" revolution by some, and the wish by others to "Join the Establishment."

Naziism was a "revolutionary" movement, until the Party amassed a plurality and nearly a majority in the Reichstag. Then Hitler saw that it was possible for the Nazis to rise to the top of German society by quasi legal means. Specifically, the German military and other arms of the German government could be made subordinate to a Hitler-led executive branch, because he also had so much legislative power. But Roehm wanted a "second revolution" to replace the leadership of the military, banking system etc., with his cronies.

During the French Revolution, the moderate Girondists (like Danton) wanted the French Revolution to end with the overthrow and execution of the King, and a return to normality under a legislative assembly. But the extreme Jacobins (led by Robespierre) wanted a continuing Reigh of Terror to "remake," not "normalize" French society. Finally, Robespierre and others were caught up in the "remaking" and guillotined, bringing an end to the Reign of Terror.

In the Soviet Union, Lenin and Stalin wanted to concentrate on building Socialism in one country (their own), while many other Communists such as Trotsky wanted a "continuing" revolution to make Communism and "international" movement.

It's actually very simple. So long as the target of a revolution/movement exists, the solution remains very theoretical: "solve the problem". During this time, everyone in the movement generally agrees with everyone else.

However, once the revolution/movement succeeds in obtaining all or part of its goal, solutions have to become concrete and realizable. It's at this point that people begin to realize that nobody was actually in agreement on what the solution should be.

Solutions end up being more complicated than expected, slower to take effect than hoped, and not as starkly contrasted from the status quo as the theory had suggested. This results in bad feelings, splintering, internal struggles, and, of course, power dynamics.

I know your edited question says you're not asking about power struggles, but the reality is that everyone who believes that their solution is right ends up seeking for the power to implement their solution. And those same people were willing to rise up against a status quo in order to achieve it, which means they are willing to revolt within the movement to achieve it. Those who actually do achieve power understand this, and do all they can to crush such attempts.

Historical examples would be somewhat fleeting because people tend not to document their betrayal of others. But one modern-day example can be found by watching Frontline's documentary "The Brothers | Revolution in Cairo", which presents a rare view into the internal dynamics of a revolution.

Old system destroyed, new system not yet established

When you observe human behavior in large groups, you will notice a large amount of inertia. Let's take for example British political system. They have a monarch, with mostly ceremonial duties. They have a parliament, elected with first pass the post voting system, and very powerful Prime Minister. This system has its shortcomings and advantages, but what is most important is that people are used to it. Average British voter knows what to expected, he may envy countries with proportional representation and president instead of queen, but at the end of the day things were rolling like that for years (with relatively small changes) and he has certain degree of certainty and stability. In the same way he drives on left side of the road, even when the police is not present, he also participates in political system even if he does not like it.

But what happens during revolution ? In certain time and place, people could get so unsatisfied with political system they would want to destroy it. Note negative part - destruction of old system (Ancien Régime) is a primary cause for revolution. What would happen after that is a realm of ideas and speculations. We could take example of American, French and Russian revolution. In each case there was a critical mass of people united by singular idea of removing the old. Anything after that was still untested speculative ideology. And more radical it was, it was more open for subjective interpretation.

As a rule, each successful revolution is followed by brief period of anarchy and "liberty", followed by rule of strong. Note that certain revolutions (like American for example) did not completely dismantle old system (for example common law), therefore this period of chaos was subdued. More radical ones (especially Russian) did away with almost everything, and after that power went to most ruthless, strongest and organized group. Strength would of course depend on lot of factors, charismatic leader could be popular today and hated tomorrow ( Maximilien Robespierre for example), trained soldiers would be more valuable then common citizens, support from abroad would be welcome, firm pre-revolutionary organization could be decisive.

In any case, former revolutionary comrades could find themselves on opposite sides of many political issues. Side which emerges dominant would seek to solidify its position and become new establishment. Others would seek to topple it (including potential counter-revolutionaries). Since these are revolutionary times and old regime is no more, new government would not have privilege of inertia and tradition. Strike while the iron is hot, and everyone with political ambitions would do just that. After all, if old rules and laws were toppled, so could be these new ones.

What then remains is new tyrants worse then old tyrants. In simple terms, new government must use more force then old government to safeguard its position and emerging political system. If they fail to do that, they could face new revolution. But in order to do that they would likely have to spill blood of old comrades, i.e. they would have to repress dissent sometimes even using deadly force. Note at that point population would be mostly weary of instability, and would welcome strong ruler or even dictator. Again, this would depend on how revolutionary was the revolution. In more moderate cases (American) revolution would only eat political carriers of its children, with certain leaders sidelined. In extreme cases we would get GULAG system.

Revolutions create instability.

Edmund Burke said the following after the French Revolution:

one of the first and most leading principles on which the commonwealth and the laws are consecrated is lest the temporary possessors and life-renters in it, unmindful of what they have received from their ancestors, or of what is due to their posterity, should act as if they were the entire masters; that they should not think it amongst their rights to cut off the entail or commit waste on the inheritance, by destroying at their pleasure the whole original fabric of their society: hazarding to leave to those who come after them a ruin instead of an habitation,—and teaching these successors as little to respect their contrivances as they had themselves respected the institutions of their forefathers. By this unprincipled facility of changing the state as often and as much and in as many ways as there are floating fancies or fashions, the whole chain and continuity of the commonwealth would be broken; no one generation could link with the other; men would become little better than the flies of a summer.

Stability does not mean that laws are always fair, or even good. It means that people know what they are. There is some certainty about what is safe or dangerous to do. To his credit Burke acknowledged that a society which could never reform would always be deservedly overthrown by its enemies.

A revolution, by definition, has enemies. At the very least its enemies will lose political power and prestige. They stand to lose much more, up to and including their lives.

Who are its enemies? They might be defined as rich people, poor people, foreigners, landowners, peasants, workers, industrialists, or anything else.

Once the original enemies have been defeated, one of two things might happen. Things might settle down into a new pattern, in which people know what's expected of them and how to make their living. Or new enemies will be identified and dealt with.

You know that this might happen. How do you know that it won't be you? One response might be to get your self-defence in first. Denounce whoever is a threat to you.

This brings in the second point, which may help to explain why purges are often wreaked by extremists upon moderates - it is about the idea of purity.

5. Sanctity/degradation: This foundation was shaped by the psychology of disgust and contamination. It underlies religious notions of striving to live in an elevated, less carnal, more noble way. It underlies the widespread idea that the body is a temple which can be desecrated by immoral activities and contaminants (an idea not unique to religious traditions).

I don't know of precedents from Ancient History, though they may exist. However I'd suggest a parallel between the Bolsheviks' successive waves of purges and the burning of heretics and witches in the Reformation/Counter-Reformation period - by both Catholic and Protestant factions. Martin Luther was very enthusiastic about putting down the Anabaptists, for example. He wanted to purify the church. Why would he decide to stop when it was mostly pure?

Revolution and Power

As Lenin famously said, the key question of any revolution is the question of Power.

Translating it into the vernacular for the benefit of the unindoctrinated: a revolution is done for the sole purpose of gaining power. All talk about giving land to peasants or factories to workers is just that - talk, the people who are actually leading the revolution have no intention of implementing anything that might conceivably detract from their power. They also assume that their differences are tactical and will wither away when they gain power, thus they "expect" (sincerely or not) the unity created by the common struggle against the Ancien Régime to persist into the post-revolutionary period.

Thus, once a revolution succeeds, the new centers of power start to fight each other until a certain stability emerges: coalitions form and fall apart as their members pursue their own goals.

A classic example would be the Russian revolution, where the clear leader, Lenin, became increasingly incapacitated by health in early 1920-ies, which resulted in a coalition of Zinoviev, Kamenev, and Stalin contesting the power against Trotsky, the immensely popular heir apparent. When they kicked him, Stalin united with Buharin to get rid of Zinoviev & Kamenev, and then purged Buharin to emerge the only leader. The contest was, of course, played in the appropriate ideological terms (like "left opposition", "right opposition" &c), but the essence remained the same - who will wield the power.

The only historical "exception" to this pattern is the American revolution, where the founding fathers recognized their differences (and thus expected a power struggle post-victory) and wanted to create the least powerful central government that would still be capable of holding the Nation together. The largely non-violent collapse of communism in the late 1980-ies is "out of scope" as it was not led by "professional revolutionaries" who could engage in "post-victory squabbles".

Moderates vs Extremists

The side that wins the post-revolutionary power struggle is the clique with the most tactical skill, not the "moderates" or "extremists".

Stalin was more moderate than Trotsky but less so than Buharin. So, in the mad world of Bolshevism, he could be labeled a "centrist".

Jacobins ruled for a mere year and were wiped out.

I am not sure Rohm could be construed as a "moderate" (to put it mildly).