Why did some nations embrace totalitarianism after World War I?
The Great depression caused much social strife- which caused extremist/radical ideologies to gain traction as they promised solutions to the problems caused by the great depression.
Warning: Very long explanation!
Communism, Fascism, and Nazism and Japanese militarism all promised solutions to the troubles caused by the Great Depression, and most nations fell under far-right ideologies characterized by military conquest and expansionism (Italy, Japan, and Germany). Communism also had their own solutions to the economic troubles by putting everyone to work in the 5-year plans. (Although only the USSR was communist at this point, communism still had many supporters in other countries- but they had already embraced communism during WWI so I would not count it for this question)
There is actually a lot of evidence to suggest that the Warmongering/totalitarian nations (Japan, Italy, Germany) were actually relatively peaceful up until 1929- right after the Stock Market crash occurred in Manhattan on black Tuesday, which was the start of the great depression. I will go through the European nations first and then Japan, which was although not as totalitarian as Germany or Italy, was a great cause for aggression in Asia due to their strong, independent army.
Germany , although having been punished by the Treaty of Versailles of 1919, gradually opened up to the rest of Europe- which was officially settled with the Locarno treaty of 1925, where Germany, Britain, France, and others settled the post-war relations, causing widespread enthusiasm for the future. Germany joined the League of Nations a year later in 1926. This can be attributed to the skillful handling by German politician Gustav Stresemann. The German economy was also helped by the American Dawes plan by 1923, and later by the Young plan in 1929, both of which provided economic aid. Here we can see that Germany was still peaceful and was starting to rebuild- but then the depression happened and the American economic aid was halted to Germany, causing much misery in the country due to hyperinflation (people's money became worthless).
The Nazis capitalized on the depression and people's disappointments and promised solutions to Germany's problems- and Hitler was a frantic campaigner who used extensive propaganda.
In 1928 the Nazi party only gained 4% of the vote share in the German election (prior to the depression), but in the next election of 1932(after the depression began), they gained 32% of the vote share. (See the connection?) Hence Hitler became chancellor in 1933 and started taking more control of Germany- turning it into a totalitarian state. People did not anticipate this and probably thought that it cannot possibly get worse- and to some extent, this was right, as Hitler initiated the building of the autobahn to stimulate the economy, which helped to alleviate the economy.
Italy is a similar case. In 1915 they were promised a great amount of territory by Britain if they joined WW1 on the Entente side by the treaty of London, but they did not get everything that was promised in the treaty of Versailles- causing them to feel cheated. This was facilitated by the fact that during the Italian election of 1919 the two biggest parties failed to form a government- causing even more unrest.
Having formed the Fascist party in Milan in 1919, Benito Mussolini promised stability and a hard-line policy to restore Italy's former glory through conquest and military expansion( though this came later). In 1922 the Fascists had their "March on Rome",- which arguably was a coup, but Mussolini was appointed prime minister by the Italian king as, according to the king, Mussolini represented much-needed stability for Italy. This caused Mussolini to gain great power and he began turning Italy into a totalitarian state- although he was initially pretty peaceful during the 1920's.
However after the depression began in 1929, Italy became more expansionist. In 1935 Italy invaded Ethiopia due to their lack of resources at home,(and partially for Mussolini to gain prestige)- causing more tension in Europe and showing the ineffectiveness of the league of nations.
Finally, we have Japan. Although perhaps not authoritarian, the Japanese War Party and the Japanese army gained more and more autonomy- to the point of near totalitarianism. Although Japan was comparable to Germany in the sense that thanks to some politicians, like their Foreign minister Sidehara, they signed many international treaties- Versailles in 1919, Washington naval treaty and the 9-power treaty of 1922(restricting navies and to respect Chinese sovereignty), and the Kellogg-Briand pact of 1928 (outlawing war) and they were thus pretty internationalist rather than nationalist prior to 1929.
However, owing to Japan's growing population and lack of resources they sought a "life-line" even before the depression- and found it in Manchuria (the region North of the Korean peninsula). Japan was dependent on trade for their well-being, Hence when the depression hit in 1929 and nations stopped trading due to tariff barriers and protectionism, the Japanese economy suffered. The War Party and Japanese army gained tremendous traction and more or less acted out of the Government's control. They then managed to stage an attack on themselves (The Mukden incident of 1931) to motivate an invasion of Manchuria- starting the Japanese expansion in Asia.
Hopefully, this gave some perspectives into why the three "Key nations" behind WW2 became expansionist and totalitarian.