If we're meant to have an equitable division of labour, then why is it that only women are naturally capable of feeding infants? (And why are only women sure that kids are really hers?)

Evolution proceeds on the basis of life or death issues. A horribly unfair division of labour where there are lots of kids is (evolutionarily) far preferable to a completely equitable division with 1 kid per couple.

Humans are not as extreme as, say, cats. There dad shows up, the sex really sucks, and mom is stranded with the kittens. That's par for the course for most mammals.

By contrast in humans there is at least a considerable amount of tension about how much work dads are going to do, and dads do wind up doing a significant amount of work. (Though less, in general, than moms do.)

Cheers,
Ben