Help/Advice about DNA TEST & child support

Dude and I were friends with benefits however I told him he was the only person I was messing with. Which is true. I ended up pregnant and the doctor told me the day I conceived. We engaged two days before my ovulation and I got pregnant the day of ovulation. When he found out I was pregnant and he said he wanted a dna test. He said he couldn’t just take my word that it’s his baby. That I understood. however more of his rules when it comes to the baby is that until he gets a dna test and the baby comes back as his (which is after the birth) he will not be involved in anything. No doctor appointments, no help with supplies, no help with groceries, doesn’t want to go to classes to prepare for baby, doesn’t want to go to the gender reveal doesn’t want to come to baby shower. Doesn’t want to hang out nothing. He also says there’s nothing for him to do anyway because the baby isn’t here. He also got upset with me that I was going to put him on child support saying I’m threatening him with child support because he wants a dna test. I told him his interest and the interest of the court are similar and that they are waiting for my baby to be born to determine paternity and for you to step up. I can’t take your word that you’re going to be an active father when paternity is made. I have to make sure my child is ok first. I believe the dna test should just be confirmation and reassurance that it’s your baby not when you decided to become accept your role as a father. So what do you guys think? All criticism is welcomed. Am I being dramatic? Should he be allowed at the birth if he doesn’t think it’s his?