Because it's great at killing things, including human skin. Seriously, my local gym has people practically sign their life away before letting them into a UV-A/B tanning booth. No way are you putting the even worse UV-C bulbs out in public. That's how people got their retinas fried at a crypto conference in Hong Kong last year.
People think I'm nuts when I wear sunglasses on cloudy days, but my eyes hurt. Idk why they don't hurt the same way sunny days, probably I don't squint when it's not so sunny.
Probably the scattering effect of the clouds. Instead of light coming from one direction, which you can angle away from to reduce intensity, the diffused light from the clouds is bouncing every which way. Which while making the intensity less, instead keeps it constant no matter where you face. I often wear sunglasses while driving on cloudy days for similar reasons.
Basically, looking at direct sunlight will obviously be more damaging, but diffused light doesn't give you a break.