Disclaimer regarding the below, my sources are limited and have their biases, and I am nowhere near an expert.
The reasons I have heard for fascism may relate. I know slightly more about "why" countries become communist, though I am still a novice in both and in comparative politics in general.
Barrington Moore, who is these days seen as a pioneer in comparative political sociology, but whose observations in their specifics tend to be disregarded today, to my knowledge, saw a connection in Germany and Japan between state-led capitalist development and the unity of purpose among various sections of the upper-classes and fascism. This manifested owing to, if I recall correctly, a sort of end-run of expansionism that inevitably led to war and to reaction "going popular" in the form of fascism. The exact mechanisms, even as I reread what he wrote on it, are still hard to parse and I think a good example of why one should look elsewhere.
More directly, I think you can paint with a broad brush and say simply this: that Germany, Italy, and Japan were either (a) relatively new, or (b) new competitors (Japan had been around for centuries, but only after 1868 decided to compete directly with Europe). They were modernizing and seeking quickly to catch up to either better-established, more powerful, or more modern countries. England, France both developed overseas colonial empires of immense size. Germany, Japan, and Italy made some gains toward the end of the imperial period with the two European Axis power grabbing up either slivers of land on the one hand, or vast deserts no one wanted on the other. Japan took advantage of a reeling and weak China to continually push onto the East Asian mainland. Ideologically, I think it wouldn't be hard to make the case that each of these three countries adopted ideas not only of nationalism, but of self-renunciation, self-sacrifice, strength, military modernization, and so on. Not that these values are bad in an of themselves, but in a globally competitive environment and in an era where warfare had found new levels of destructiveness that early fascist thinkers opted to
glorify, it can get very ugly. The Great Depression and the need to appeal to something that could paper over class conflict and economies that could not address the litany of issues they were left with could, some theorists say, lead to a sort of anti-class idealist anti-communism--fascism.
Hannah Arendt also had some thoughts on authoritarianism in general, but my single reading of
Origins of Totalitarianism did not grant me a coherent picture of what she was trying to say. In one instance, she pointed out how Germany and Russia were both situated so that they had to imagine land empires in the forms of Pan-Germanism and Pan-Slavism, rather than vast colonial empires. I think part of her point was that totalitarian governments treated their own citizens as they would colonial subjects, I don't know. In another section she discussed how the English party system was different than what she called the "Continental" party system. The latter, with multiple parties, allowed for such bickering that there was a demand for apolitical parties--parties that prized the nation itself as an ideal above politics. One gets the impression that she prefers the more straightforward class- and ideology-based politics of Great Britain.
As for comparing this to the Allies, what can at the least be said is that, in the case of England and France, even in their darkest days (outside the Terror), they both developed histories wherein--as Barrington Moore again will point out to us--arbitrary authority was checked. In both cases, with the literal death of a king. England is particularly notable in that its historic reliance on naval power deprived it of a certain degree of domestic repression that a domestically-stationed standing army might have given it. There are probably also certain cultural and economic reasons why fascism did not succeed there, which likely merit examination as well. In the case of Russia, we will, like Moore, pair it with China in that both were large land-based empires ruled in a centralized manner. Both underwent collapse with some comparable stages--specifically, a liberal government takes over following the collapse of royal power, but fails in balancing competing demands, so is swept up in a tide of further unrest. The Chinese descent into communism happened at a substantially slower pace than the Russian did. There has been some writing on proto-fascist movements in Russia following the loss to Japan in 1905, but I'm unsure where our argument would start with why they did not succeed. The most obvious answer would be that there was substantial popular discontent directed against not just the upper-classes, but against authority in general, and that the Bolsheviks made the proper bet in deciding to "side" with the peasants early-on in land issues (if I remember correctly) and that the reactionary forces lacked the manpower, tactics, and "objective conditions" to win a civil war.
