Germany was one of the least militarized countries after WWII. They were kind of scared of themselves.

Rather: the "victorious" countries of the Second World war were afraid of a re-militarization of Germany. On the other hand, they wanted to re-militarize the Western part of Germany just a little bit so that West Germany could become part of the NATO.

Quite the contrary; up until the end of the Cold War both German states were highly militarized. They were quite happy to be able to roll back a lot of it after the reunification though.