My normal disclaimer that I have a doctoral degree in law, taxation, and specialty in history of the Common Law, but I have read widely on the French Revolution (which gave life to this quote) and revolutions in general.

To begin, the original quote is “A l'exemple de Saturne, la révolution dévore ses enfants,” which translate to “Like Saturn, the revolution devours its children.” Goya’s painting would come some thirty years later, but it does give a visceral feeling of the line. This was from a publication in 1793 by Jacques Mallet du Pan, a royalist and anti-revolutionary, so while not presaging the general violence of the revolution, it probably presaged the Terror, depending on one’s starting point for the Terror proper. (Source in original French facsimile: https://archive.org/details/considerationssu00mall_0/page/n3/mode/2up). The Terror was, as your probably know, when the French Revolution’s foremost symbol, the guillotine, became insatiable, and factionalism fed Danton’s head through its maw, followed by Robespierre, and many many others notable but who need not be mentioned here.

Revolutions tend to devour their children because once the immediate matter of overthrowing the preceding power structure is accomplished, the people involved with that overthrow tend to begin realizing that they do not have identical (or even similar) ideas of what should replace it. Once the group (or a coalition of groups bound by an immanent and tangible goal) achieves their goal, factions either develop or reappear.

The French Revolution was fomented in large part by a vast number of clubs and later factions or parties that worked together initially, then became bitter rivals for solidifying power in the vacuum left by the regicide. Danton, for example, may have coined the Terror by legislatively instituting “terror as the order of the day.” (See, e.g, https://revolution.chnm.org/d/416/). Robespierre and Saint-Just, afraid of the Dantonists (as Danton’s group was called) would take power from their group, the Jacobins. Even earlier, all three had conspired together to destroy another group, the Girondists.

The Irish War of Independence provides another great example of those (Modern Ireland by R.F. Foster is an accessible gem that handles that period in the context of a holistic view from 1600-1972). The Irish War of Independence concluded with Michael Collins and company entering into the Anglo-Irish Treaty, which created the Irish Free State recognized by Great Britain, but which came with the rather controversial caveat that members of the new Irish legislative body must take an oath of allegiance to the sovereign of the United Kingdom. (Text of the Treaty at https://www.difp.ie/volume-1/1921/anglo-irish-treaty/214/#section-documentpage). This immediately caused the Irish Civil War, fought by pro-treaty and anti-treaty forces. The pro-treaty forces, probably most visibly embodied by Michael Collins, argued that the Treaty was necessary for a war they were not necessarily winning, and as such gave the Irish Free State the “freedom to gain freedom.” The pro-treaty forces were therefore a coalition itself: some thought the goal had been achieved, and opposed further fighting; others thought that practical necessity demanded entering into the treaty or losing entirely. Anti-treaty forces were even more diverse, going from simply nationalists that disavowed any connection to the UK, to socialists like Peadar O’Donnell, and an assortment of other small idiosyncratic group. The Irish Civil War was particularly tragic because of how personal the split between pro- and anti-treaty persons was. Comrades-in-arms were quite suddenly fighting to the death. Michael Collins is believed by some to only have been successfully assassinated when he was because an anti-treaty Irishman recognized him from serving with him during independence, and put together an ambush out of knowledge of his value. (Liam Neasy, Brother Against Brother).

Even the United States, which has historically been held as a rather peaceful Revolution, certainly cannibalized both its ideals and its people, specifically through the creation of political parties. Washington made an immense effort to make the coalescing parties have a stigma, most notably in his Farewell Address. The creation of parties necessitated rapid amendment to the Constitution, such as the Twelfth Amendment—the electoral college had to distinguish between votes for president and vice-president or else there would be an extreme and unanticipated tension since the two-party system, even nascent, would cause opposing parties to occupy each post. You also have famous cases of the Burr-Hamilton duel, which embodied the sort of tension that had built in Washington between the Federalists and the Democratic-Republican Party.

The short answer appears to be that it is easier for a diverse group of people to band together in the unity of wanting to destroy something, and much, much harder to keep those same people together to build something new when they have all known violence and a desire for power.