Because the accidents have all been with very old designs. Even at Fukushima, in the face of a 9.0 earthquake and tsunami, reactors built in the 80's instead of the 70's got through it all just fine.
Because climate change is turning into such a desperate problem that we can't afford to leave any solutions on the table. And nuclear works quite nicely with solar power...nuclear all the time, solar for extra peak load during the day.
Nuclear is not just the side effect of a weapons program. It's an amazing energy source. With the most advanced reactors, all the energy you need for your entire life can come from a lump of fuel smaller than a golfball.
It's very sad that our first use of this technology was to kill people. Perhaps if we hadn't figured it out in the middle of WWII, things would have been different, and climate change would be a hypothetical instead of an imminent nightmare.
You are asking the question this way hoping someone has a better answer - they don't. Nuclear is our best option for making clean and reliable power that will get us to that next best option. Some of the new designs out there are quite amazing feats of engineering.
Nuclear power in its current form presents tremendous, potentially country-altering downside when things (can and will) go wrong.
Is this really the best humanity has got -- the side effect of a decades-old weapons program?