Notice I didn't say AARP members. I know many AARP members who only join to get the discounts. I believe that to be true for the majority of members. AARP gets their clout by their large number of members and being able to present them as a monolith when it isn't close to being so. And as the "leading senior organization" they get immediate, free, and regular media coverage to push their management agenda.
If SS were privatized (fully) within 2 generations there would be no need for AARP. They are opposed to privatization for the simple fact that it posses a serious threat to their existence.