I think they meant the opposite; physics throws things out as soon as there's a need for exceptions, and there are examples of that.

Well, once they have a better explanation.

We know that mass of matter does not explain even half of the mass observed in the Universe; we haven't thrown out the explanations of mass and inertial gravity, but have a placeholder called "dark matter" to refer to the missing explanation.

Maybe we’d say “physics” is really just the delineation between things we have an accurate model for and everything else (the exceptions?). Theoretical physics would be the search for the “why” of everything, inside and out of that line in that case.

I’m not a physicist, so I’ll let them pipe up on how much is in and out of the descriptive line, and how much is in and out of the theoretical explanation line. But I don’t know many physicists who think we’re close to “done” with either endeavor.

I'm not a physicist but I've always seen physics as a bit hand-wavy myself.

Dark matter is a great example.

Our understanding of gravitation didn't cleanly apply at ultra-large scales so we had to add a massive fudge factor.

You can't "go faster" than the speed of light, but space in between things can expand faster than the speed of light.

It seems like things that are "settled" regularly get an "ope, but except for this special case..." treatment.

There is no handwaving involved. The layman explanations of these phenomena are not that good. The quantitative derivations that leads to those results are totally fine, but hard to follow without deep knowledge of the subject.

Physics education sometimes aligns with historical evolution of the theories, mostly because that builds intuition and because the mathematical founsations of the improved theories need to be taught first. That leads to the "but in this case..." moments, but you need to realize that what you get taught as a "fix" is practically always a careful evolution that also reproduces all predictions from the less complete earlier theory.