Of course they don't always; certainly IRV is sometimes mechanically better. I believe we can construct examples where FPTP would happen to work out better given the same honest votes, although I do think they're more contrived - see below for details. I am more worried about what happens in practice, though; as I said, people understand with FPTP that they need to vote strategically and understand how to do that.
Contrived scenario for FPTP picking the Condorcet winner while IRV fails to:
Back to the "which theocracy, or do we just tolerance?" question, but now each religion has at least two candidates and secular tolerance has a bigger constituency.
19% S, ...
16% A1, A2, S, ...
15% A2, A1, S, ...
14% B1, B2, S, ...
13% B2, B1, S, ...
12% C1, C2, S, ...
11% C2, C1, S, ...
FPTP picks S, sort of by chance, which is also the Condorcet winner. IRV consolidates the C votes behind C1, then the B votes behind B1, then the A votes behind A1, then discards S.
I think that works out, FPTP makes the right choice for sort of the wrong reason while IRV makes the wrong choice. But I do think the much bigger concern is FPTP-with-strategic-voting behaving better (or at least no worse) than IRV-with-whatever-happens-in-practice.