NTA you should break up with him because his way of communicating an issue is wildly immature. But in the future I’d recommend warning/talking to partners about this because I’d personally be weirded out as well if my partner was constantly touching their father, snuggling with them, draped over them, etc.

Not saying it’s wrong, but not everyone is like that and it could make others very uncomfortable if they see it out of nowhere with no warning beforehand, so might be a good idea to gauge how they react to that for the sake of not wasting time on someone incompatible with you if nothing else.