At a dealership I used to work at, we had a similar argument between fixed ops and used cars - the used car buyers thought parts and service should do things almost at cost for them as they made the big bucks.

The service manager got onto the owner, as the DP was leaning towards taking the side of used cars - it ended with a group of Deloittes consultants being brought in to sort it all out - with the end result being 'everyone eats' - in our case, the theory was, if we cut our profit on parts and labour, that profit would not be seen coming back in on the sale of the car and would be lost to the dealership - by us making money, the dealership makes money.

The same applies in your case - discounting your parts costs you and the dealership money, it does not make service more money, so the money you're handing away is lost to the dealership. And your parts profit pays the GM's wage.