Am I wrong for cutting my childs father off completely?

I’m pregnant by this guy I was talking to, we weren’t exclusive or anything. He begged and begged for me to have an abortion i contemplated it ALOT, but it just doesn’t sit well with me and I could never go through with it. he’s been so wishy washy he’ll say he’ll be there but then say he wants to sign his rights away (my brother offered to adopt the baby so he can do that) or just simply walking out. Like I cant even tell you how many times he’s gone backs and forth and we’ve only known I’m pregnant for a month. Since I made the decision to keep the baby I told him do as he please. So one day we talked and we came to common grounds on coparenting and we were ok even talking about baby stuff and names. Not even 2 days later he text me saying he can’t do this even had his mom call me out the blue to tell me that her son isn’t ready for this. I told her I’m not forcing him to do anything and he can walk away. That was a week ago and now I got a text yesterday about him saying when the baby is born he’s going to take me to court for joint custody and rights but also in the same message asking me to reconsider abortion AGAIN. I don’t think this is fair for me because he’s been fucking with my head ever since I found out I’m pregnant. I’ve been diagnosed with depression and anxiety from all this. I have nightmares of my baby being taken away. I just don’t know what to do I don’t want to be mean and not let him see his child but I can’t handle this stress. I’m tired of crying 24/7. So I was thinking to not post my baby on socials or anything about my pregnancy at all (because we have mutual friends, he’s blocked on everything) and not giving him any updates... just completely shutting him out. I even thought about telling him I had an abortion so he could just leave me alone. Would I be wrong to do any of that? I just want to be at peace and start enjoying my pregnancy with my family and friends.