We have enough experience with ZFC that I think we can say it is consistent with some confidence.

This isn't too surprising --- I don't know if there's a way to say this precisely, but morally speaking consistency is "easy". Any collection of axioms is inconsistent only if the negation of one of them is a provable consequence of the others. Thus for a system to be inconsistent there must be some special interaction between the axioms, and again, I don't know how to say this rigorously, but to me that says consistency is "normal" and inconsistency is "abnormal".

What people who ask this question sometimes miss, though, is that there is a difference between consistency and soundness. ZFC could prove false statements about the natural numbers but still be consistent. I made this argument here. In contrast to consistency, soundness is not generally to be expected; in order for a collection of axioms to be set-theoretically sound, every one of them must be true. If the axioms were chosen randomly this would be highly unlikely. So the question becomes "what grounds do we have for thinking that ZFC is not merely consistent, but also (to keep things simple) arithmetically sound?"

I personally don't think we have strong reasons to think ZFC is arithmetically sound. Although a (purported) philosophical justification was developed later, when Zermelo first presented his axioms his justification was wholly, and explicitly, pragmatic. They weren't chosen because he thought they were "true". Maybe the thing that bothers me the most is that virtually all of normal, mainstream mathematics can be formalized in much weaker, essentially number-theoretic systems that do have a clear philosophical justification. What ZFC adds to this is a raft of set-theoretic pathology. To me, that suggests (but only suggests) that ZFC might not be arithmetically sound.