The fact that Finland ended up being finlandized was because the country had allied with nazi Germany from 1941 to 1944 in the so-called 'Finnish-German Brotherhood of Arms' ... Finland believed that Germany was the powerhouse of the future.
Finland took advantage of the old adage, "The Enemy of My Enemy, He is My Friend". Finland had just come off a loss against the Soviet Union in the Winter War, mostly through inaction on Britain's part. An irony of that is the Soviet Union set up the invasion by having Finnish artillery kill ten Soviet soldiers.

So in 1941 Finland could've stayed neutral, or they could've contributed to the effort against the Soviet Union. They chose to launch a campaign to regain several regions lost through Soviet actions, since it was a better idea. Germany was sweeping eastward, and the Finnish wanted to get back what was theirs. While they started a 'Finnish-German Brotherhood of Arms', it wasn't because they agreed with the ideology, it was simply because joining the Allies meant they would be working with the Soviets, who took alot of their land.