Questions: Girl's Behavior

So guy met at a friend's party starting to date - just coffee so far - has said twice randomly he isn't the sort to cheat in a relationship. Now this is entirely unprovoked, we weren't talking anything remotely along the lines of cheating or even sexual and yet he spouts this off. To me it's a major red flag because why say this unless he's done it before or been accused of it

You can come and go but never bring a man with you. If you are in a relationship with a man you can't bring him and you have to leave if you want to move in with him. You also have to leave if you want to raise kids with a man and or have a boy child. If you leave for any reason for any time period you can always return but not bring a man or boy child with you. Female to male transsexuals can be allowed but no male to female.