When we burn fossil fuels a huge volume of hazardous waste just goes into the environment, and we know what it does then. With nuclear there is also a huge volume of hazardous waste, but at least it remains spatially consolidated and in our control. The consensus best solution is deep burial. Sure we might run out of space and create nuclear "landmines" over the very long term, but it's a preferable tradeoff to the much more imminent threats of the global warming.
Greenhouse effect, ozone depletion, poisoning the hydrosphere and biosphere, etc; not going to dignify the question with further details.
I don't understand why one wouldn't believe in the environmental dangers of conventional energy sources but be hyper concerned about the "environmental catastrophe waiting to happen" from nuclear energy sources.
https://en.wikipedia.org/wiki/Radioactive_waste#High-level_w...