Nazis are all over Eastern Europe, it's something that happened to a certain segment of young men after the end of communism, was born largely from imported racist material from the US and Western Europe, and was fed by inspiration from UK and Italian football hooliganism (Casuals, Ultras, etc.) and "National Socialist Black Metal" which is actually a genre of music. People involved in these scenes formed gangs that developed into militias, some of the people in these militias were the children of oligarchs and politicians, and they used those gangs to enforce local collection rackets and to commit political violence. This isn't a story about just Ukraine, it's more a story about Russia, Ukraine, and Poland.

Having oligarchs connected to Nazi militias was an ideal way for the US to get money and arms into Ukraine to fuel the 2014 coup. It was simply a marriage of convenience, but one that propelled Nazis into a lot of power on the ground and in some of the institutions of Ukraine. Ukrainian Nazis think of Russians as a racially mongrelized people, and were happy to help wage war on Russian speakers in Ukraine as a war of racial cleansing. Also, their newly heroic status in some of the conservative mainstream quarters of Ukraine (combined with the forcing of Russian speakers to the East), allowed them to racialize Ukrainian identity. As we poured money and arms into the country, the Nazi militias became more and more official, and more and more the direct recipient of those arms.

The rise of the Nazis has largely been inflicted on Ukraine by US manipulation. They're just another instance of "freedom fighters" and "moderate rebels" that we fund to get what we want. When Ukraine voted for an actor who played the president on TV, they were taking the same desperate stand against the powers-that-be (in this case Russia and the US) as the US was when they elected Trump (against the Democrats and Republicans.) They were voting for peace, and an end to corruption. It didn't go well.