Let's start with something simple. The Definition of Horror.
Jaws satisfies this definition. It is a movie that elicited so much fear with audiences that it drove down beach attendance for years after it's release. So much fear that it changed forged an entirely new identity for sharks on a whole. One where they were human hunters that were out to get people. It is a real psychological issue that has been dubbed "The Jaws Effect".
Even if you want to get more specific and use WSD's favorite source, wikipedia, we can. Here is Jaws under the "Horror Film" page. Specifically the sub-genre it helped define, Natural Horror.
It's almost like it fits every definition for a horror movie and is literally categorized as one.
The common argument is that it is more of a thriller. But it can simply be both of those things. In fact, you could even argue against it being a thriller or psychological thriller based on the classic definition.Dave would actually have a better chance using this argument if he used it specifically against American Psycho OR 2 movies he didn't name, "The Silence of the Lambs" and "Get Out".
It might not feature a lumbering food with a kitchen knife or some ghoul or goblin, but it is no less a horror movie than any of those. An inescapable force of nature that strikes fear in you while watching that stays with you every/any time you set foot in the water.