That's an overstatement of a mathematical theorem. Arrow's theorem says that for approval voting, yes there are some cases of people's preferences for which one of those conditions fails. Nobody is claiming that approval voting satisfies all of those conditions, so nobody is provably wrong.

People are claiming that approval rating works better than first-past-the-post in many important cases, such as introducing a moderate candidate into an established two-party situation. Arrow's theorem does not contradict that.

Arrow's theorem only applies to ordinal voting systems. Approval voting is a cardinal system to which Arrow's theorem doesn't apply.

So yeah... Math and everything! https://en.wikipedia.org/wiki/Cardinal_voting

All Arrow's theorem does is say that an ordinal voting method can't simultaneously meet a certain arbitrary collection of criteria.

It doesn't prove that any of those criteria are necessary. Independence of Irrelevant Alternatives, for instance, is especially problematic.

Finally, Condorcet methods don't even fail Arrow's Theorem when there's actually a Condorcet Winner (which is pretty much always given enough voters).