Why do teeth hurt after bleaching?

No one knows for sure, but it maybe the result of temporary dehydration of the teeth. Teeth have water content and dehydrated teeth can become sensitive to air and cold water. Bleaching solutions often use hydrogen peroxide or carbamide peroxide as their active ingredient. It could be that the peroxide is replacing some of the water in the teeth and then evaporating, leaving freshly bleached teeth temporarily dehydrated.