Some good answers below already. I think the anti nuclear movement already started before Chernobyl. I believe it was one of the founding ideologies of the green parties (the danger of high CO2 emissions was not yet front of mind for a lot of people back then). So the opposition to nuclear energy kind of laid the foundation for the modern (European) green parties. But these were all young people back then (in the 70s) and a they have now become the dominant generation in politics. So just like in any other country the 50+ years old are in charge and that cohort in Germany happens to have fond memories of opposing nuclear energy.

And just a little side note because I've looked it up recently: EU produces about the same amount of nuclear energy as the US - and that's despite Germany shutting down all reactors. So it's not like the US or any other region has a much higher usage.