Maybe we mean different things by "critical thinking"? To me, an essential part of a proof is checking that it is correct yourself... as opposed to "learning"

Maybe we mean different things by "critical thinking"? To me, an essential part of a proof is checking that it is correct yourself... as opposed to "learning" it i.e. taking it on faith, believing it is correct because someone said it was. (Of course, in practice you can't verify everything yourself... but nonetheless that's the idea of mathematics, in theory). Is that not the purest form of critical thinking? OTOH I suppose when a proof uses a clever change in perspective, to show that it must be true (such as non-constructive proofs), it refutes many possible objections without ezplicitly considering them. So formulating those objections (or "criticisms") isn't needed.