Just to be devil's advocate here.....I can think of two advantages(at least for me) playing with a non pro can have over a pro.

The first is the luxury of time. One of the biggest drawbacks to pro sessions for me is the inability (or at least the large cost) of doing a truly extended session. My longest pro session ever was about 5-6 hours while my longest with a private play partner was more like 18.

The second is the likelihood of far more intimate activities taking place in a private vs pro session (at least in North America)

Of course this presupposes a skilled amateur and an established relationship. Both of which I have been lucky enough to experience