Should I let my childs father claim him on taxes?

This is our first baby and first time doing this. We aren’t in the best space and I feel as though I take care of majority of our babies expenses since he’s been here. When I was pregnant we both worked but I owe back taxes. I’m just not sure if he should have his social security number. Or let him have any money out of the taxes. Or is that selfish? Also how do I tell him non don’t feel comfortable with it without starting a argument