Nowadays it is mostly two things.

The 1st reason is nuclear waste. Germany is more densely populated than the US so you can't store it far away from humans. The solution tried before was to just store it deep underground. Turns out that might even be worse than storing it on the surface as it turned out and it has been a total disaster (see https://en.wikipedia.org/wiki/Asse_II_mine). There have been more cancer cases in this region compared to neighboring regions as well, which might be linked to it. It is now planed to retrieve the waste again and store it somewhere else. Where is currently not known afaik. The whole thing costs billions of Euros already and is going to cost even more and didn't even deliver on it's promises. So for that reason alone wanting to produce more nuclear waste when we can't even deal with what we already have is obviously unpopular.

The 2nd reason is cost. As shown above the storage of nuclear waste has been an expensive fail for Germany, but it doesn't end there. We don't have any nuclear reactors left, so we would need to either reactive existing ones (expensive as they haven't been maintained for continuance operations) or to build a new one. How well that works we can see in either Finland or the UK... both have huge cost overruns and aren't even on-time. I think we had enough of those projects (BER, Stuttgart21) that another one that would likely end up like this is nothing anyone wants. Building more renewables such as solar and wind together with energy storage and gas/hydrogen power plants as backup is just a lot cheaper as we don't need more base load power plants, but ones that are a lot more flexible and can be turned on/off quickly depending on solar/wind output. And any new gas power plant is planned to also work with hydrogen, which can be produced when we have too much solar/wind and then act as the storage medium. So basically a long term way to store energy that is more flexible than batteries (at least on this time and size scale).

In the past reasons were different, but those aren't really relevant now.

Another relevant note here is that Germany is heavily investing in nuclear fusion, which is probably a better use of funds. https://www.dw.com/en/nuclear-fusion-germany-bets-billions-o...