Not really hard: nuclear power generation uses radiation and radioactive material, but tries very hard not to release it. Coal power generation burns a substance that contains a small amount of radioactive material, and makes no effort not to release radiation.

It's not that surprising. We're burning a rock we dug out of the ground and turning it into a vapor. Rocks found underground contain some amount of natural radioactive material, for example granite/marble tend to be higher in radiation. If you burn that into a powder and put it into the atmosphere it'll spread around and expose the nearby area to very slightly radioactive pollution.