My girlfriend wants to pretend that my son doesn't exist.?

You shouldn't be dating someone who wants to pretend your son doesn't exist. That's her hang up - not yours. It's good that you recognize this now and move on because I don't think she'll get over it. Just tell her that that since she would rather pretend your son doesn't exist it' probably best for all of you if you don't see each other anymore. Then be open to meeting other women who would be more welcoming of your son.