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.