So, simply saying, "no" doesn't make the other guy wrong. OTOH, resting your argument on something that simply isn't true, does make you wrong.
There are beliefs about the supernatural IRL. But, while the beliefs exist, the supernatural does not. The definition of supernatural you want to use is based upon the non-existence of the supernatural, making it useless in a setting where magic and other such forces actually exist.
Obviously it doesn't work at all, or we wouldn't have these discussions.
The scientific-leaning definition from RL is useless in fantasy, because the whole world may well be supernatural. Trying to build the same sort of definition in the context of a D&D-like fantasy setting where spells are repeatable, testable, phenomena would, conversely, make magic natural, even mundane.
We'd need a definition better suited to the genre. Like, instead of invoking scientific or natural laws, base it on mundane, everyday experience. Even then, it would probably only work if the supernatural were sufficiently rare to avoid being a mundane part of everyday experience - something D&D makes difficult, since anyone, in theory, could acquire a casting class...
If we were to root the mundane in the everyday, and conceive of the supernatural as deviating from that, then scientifically explainable, but very rare events, like a solar eclipse, meet the definition of supernatural (oh no, a giant serpent is devouring the sun!). Not exactly inappropriate to genre.
IMHO, D&D would benefit from a line like 3e drew between (EX)traoridnary and (SU)supernatural, with the ordinary or mundane a third baseline category. If we consider the mundane to be ordinary, everyday things, that literally anyone can do (if not particularly well) any time, then the extraordinary can be similar things done much, much better, and the supernatural would be things outright impossible.
So, for instance, anyone can hop over a low obstacle or across narrow ditch or the like, a stronger, more agile person could clear greater obstacles - so if you're extraordinarily strong/skilled, you can jump great distances, even beyond what might be scientifically impossible outside a fantasy world. Superhuman feats aren't off the table, if they're what humans do, but more.
But, you can't fly. ( Maybe you could stick feathers to your arms like Daedalus and Icarus, and fly that way, IDK. )
When a huge barbarian leaps over a castle wall, that's extraordinary, he's really strong, he's doing something ordinary people can do (jump) but way more so, because hes way stonger. Close enough for fantasy physics. When the bookish guy in robes casts a Jump spell, OTOH, he may be jumping the same distance, but he does it by chanting and breaking cricket legs, not by flexing huge muscles and taking a running start.
And that's a funny thing about these discussions. Supernatural or magic is often held up as needing to be far more powerful than the mundane to be "really magical," but how you do something can make it supernatural, or not.