I may be wrong but....

Hello I have a question. This is my first child as well as my child’s father and today I brought up something I noticed and it started an explosive argument between him and I. He took off work because we just had a baby a week and a half ago. We do not live together so he has traveled back and forth to my home to see our son. Although he comes everyday or every other day, he spends a max of 2-3 hours. That’s it! The rest of his day is spent chilling with his guy friends watching the games, going to strip clubs, and just overall attending different things that aren’t of any importance (in my eyes at least). So I brought up today that although he comes out here to spend “time” he’s spending the bare minimum and kicking it with his friends and doing what he wants. I told him I felt like the time he took off work should’ve been spent getting to know his newborn son as it is a “paternity leave”. I’d try to enjoy every moment off work instead of slacking on time spent with my child. When moms take maternity leaves we don’t use it to party, vacate, and do other things that aren’t important. We spend that time nurturing and getting to know our newborn child. He’s 100% allowed to spend the night, my parents allow him so he can help with the baby. He has spent 1 night so far.... And when he did come that night, he was trying to get out of staying the night although he had told us 2 days prior he was staying the night. Although he did end up staying the night, he was so anxious to leave and left by 7 am...... And today he came to pick us up so we could take the baby to see his dad. He picked us up at 5 Pm (ish) and we were gone from his fathers by 8 pm and he was ready to drop us off and go watch the game with his friends. He could’ve easily watched the game here while still being with his son. This is what started the argument. Because I mentioned that. And we argued now he’s downstairs watching the game with our newborn beside him. Dont know if I’m nagging or if he’s truly half assing and I have a reason to be complaining ? What do you all think.