Start ignoring it. I know, I know, not the thing we should be doing.
You need to put up boundaries for acceptable behavior from your parents. If they are treating you like ****, you just don’t respond to it. Let them know that you wont respond to them treating you that way, and go about your life. Make sure you’re respectful, but not a doormat.
You father is being unreasonable. More you respond to it, better he’d know to continue that (mostly subconsciously).
DO NOT marry your cousin just because of this. Wait until he calms down. In the meantime, keep talking to your mom about this issue, as well as the “fears” your dad expresses about you. If you make sure that she understands where you are coming from, she might try explaining that to him. And it might work.