Is it wrong to not put my child father on the birth certificate?

We had been together 6 years & engaged at one point we tried for a baby for around 2 1/2 years never happened. January we break up bad he wanted nothing to do with me but I find out I’m pregnant that same month. Tells me for 5 months to get an abortion I tired to include him give him updates he rejected me every time. Around 20 weeks he goes to the drs appointment for the first & only time for gender scan. He slowly became more interested( by talking to me on the phone every once and a while n asking about baby here and there) which I thought was great for our daughter everything is good until I bring up the birth (I’m 37 weeks now.) I wasn’t going to place him on the birth certificate, I let him know so he’s not surprised. He’s flipping out, at me telling me and everyone I’m the villain in the situation all his friends/family hate me. So now he’s not going to the birth at all.

My reasoning is he has a bad track record as a dad. He has a 7 year old son which he hasn’t contacted our whole relationship not once. Im very concerned he will be in and out. I’d be happy to place him on after a few months of him showing up or he can do it himself (which already sounded like a problem since we aren’t living together). I believed it was all the 1st baby mamas fault he had no contact but now I know other wise unfortunately. I don’t want to keep him from being a dad at all I’m encouraging it I have been since day one, n trying to plan coparenting. but if he’s not going to be there and I’m doing 99% of the work (I bought Everything haven’t received any $, went to every appointment besides one alone & was pregnant alone. And the thing is I’m not asking anything from him but to show up to build a relationship with her) I don’t think it’s fair to add him just yet. He’s already saying that he’s just not going to show up because he hates ME so much which is a really big red flag to me because I can’t remove myself entirely from our daughter. That was the same excuse with his ex too that’s why he doesn’t see his son. Lastly I’m really disappointed he won’t be there for our daughters birth, I have a doula so I don’t need he support but I think it a very important time to bond with her especially since he hasn’t be there the whole 9 months :/