My nails get soft when wet. Also the dish soaps are very strong,
and are a surfactant, meaning they defat skin and get into pores etc. I vote for the dish washing soap...Try wearing a glove from now on and see if that helps!

I have one finger on my right hand, that got severely pinched between rocks while gardening. Something happened to the growth plate (this is the same finger my Dad accidently closed in a car door when I was small--so it was damaged once already)..Since that more recent pinch, there is a deep vertical groove in it, about 4 cm wide, and that part is thinner now, and constantly splits! Looking at it on end, it is also curvy. I have to keep it now, trimmed really really short. It is a total pain in the "you know what".