[bawolff]

As far as axiom of choice goes, they were probably referring to https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

Whether or not it is "wrong" is in the eye of the beholder. Why should infinite things be intuitive? After all even "real" things in the universe are highly unintuitive - e.g. quantum mechanics sounds obviously "wrong" at first glance.