1. Nuclear plants are very expensive and some projects have been pumping taxpayer's money. I suspect they are not so easy to conceive, build and maintain as other sources of clean energy. Especially since they become a security issue when they get old.
2. The problem of waste management has always been a problem. I hear it argued that it is a solved problem but certainly having this problem lying since the beginning of the industry has not helped not build trust.
3. The nuclear catastrophies have been overblown because they were more spectacular and a new thing affecting lot of people in a short period of time BUT it remains that it is hard to trust people that thought building a nuclear plant in an island that is the victim of dramatic eathquakes and tsunamis a good ides AND the problem is that it fucks up an entire area for who knows how long ? That is certainly scary, no need for oil producers lobbying there to explain distrust.
4. Is there even enough uranium for the world ? Is is sustainable to invest loads of money into systems whose fuel is on foreign countries that you have to dig up ? (so according you gathered by now I am not pro-oil. Keep it in the goddamn ground)
5. It is a single point of failure. Thank god no terrorist thought of "landing" a plane there. It's broken ? No power for an entire region.
6. Finally, but this is a minor point as those considerations may be a luxury during our climate crisis, the technology lends itself well to despotic elite rule, everyone depends on who can secure control of a little army of skilled workers and engineers. Those control the energy supply would have tremendous power.