A new Guy I’ve been seeing want to be there for my sons birth.

Me and this guy haven’t even been together a month yet and he already wants to be there for my sons birth and of course I said no. Plus he’s not even the baby’s father and even the baby’s father isn’t going to be there because he’s a dead beat. Is it wrong of me setting such a boundary? Also he’s already told his mom we’re seeing each other and his sister. I also haven’t wanted to use the terms boyfriend and girlfriend yet either because we literally just started going out. He also talk to his sister about me not wanting him at the hospital and she said “Are you sure she’s your girlfriend?”. Like what??? Also girls I’m almost 30 weeks pregnant and a FTM. So what’s your advice?