Him arguing with a woman just makes her feel validated. It's like you jokingly bring up a complex topic to a child and they try to imitate you and sound smart when really it's just cute and silly. But doing that unironically? You're just arguing with a child who says cute silly shit and will never be capable of more than that, which makes you the idiot for participating. He can beat her dead to rights and she, like the child, will just say some cute silly shit and to her it seems like a valid rebuttal.