pawsplay
Hero
The problem I have is that he is claiming that because Batman has "normal guy" as an origin story he can never be thought of as being extrahuman or superhuman unless something objectively supernatural happens to him.H is belief is that the supernatural requires the supernatural to occur. Batman can't be a superhero because an alien never gives him a magic ring, or because a radioactive spider never bites him.
In other words, you can never be Beowulf, because a wizard never makes him magical.
You seem to be equating fantastical with supernatural in a way that I think a lot of people, including myself, are unwilling to agree to. In a sense you're saying that because they do what normal people do not do, can not reliably or feasibly do, James Bond, Sherlock Holmes, and Robin Hood are supernatural. I would say they're unrealistic, just in a very realistic way.

Many characters with supernatural powers, like Beowulf, have natural origins, while others, such as Perseus or Lancelot, have supernatural origins but no overtly magical powers. Batman is a modern myth, an embodiment of American-style humanism and heroism. If you take away his Puritan work ethic he ceases to be a superhero. Simply equating him with someone like Beowulf or Lancelot makes Batman not Batman, as surely as Perseus ceases to be Perseus as soon as you say his father is not Zeus.
Batman cannot win against Superman and the like because he is superior by nature, or the whole story breaks down. Batman wins despite being purely human because of his tremendous character, will, and work ethic, not to mention a little luck. If you stat him up in RPG terms and make him literally beyond human, you have gone astray. Moxy is not a superpower. Batmans is the king of moxy. That's why he wins. he's Jack the Giant Killer, he's Aladdin, and Little Orphan Annie, not Beowulf, Lancelot, or Perseus. He may be a billoinaire, but as an orphan and a kid from a rough town, his origin is that of scarcity and necessity. He's not Lancelot, he's Percival; his chief weapon is the clear-sightedness of spiritual certitude. His nature is common, and his circumstances are the product of chance, or destiny.
The reason he and Superman are a popular teamup is because they are alike in relying on their determination and moxy. Each one regular defeats foes above their weight class, whether it's Batman versus Lady Shiva, or Superman versus Zod. That's why those stories work. The Kryptonian and the American are alike in being unflinching, and those teamups hightlight that commonality, as well as their relatives strengths and weaknesses.