Here's a vote for it being upbringing, not biological at all, though very culturally prevalent. My husband was raised doing house-cleaning chores, and he can tell when something's messy/dirty/needs-to-be-cleaned in a way that I (female, not raised doing chores) can't until it's explicitly pointed out to me by him ("...what do you mean, what needs to be cleaned up? Can't you see the table is full of dirty dishes?"). I have the lack-of-dirt-radar that gets made fun of in men, and he doesn't have that. And he does rather more of the household management (and probably more of the housework period) because of it. My sister (also not raised doing chores) and her husband (raised doing chores) have the same dynamic. (She also has a much more demanding job than he does.)

Childminding tasks/management I do much more of, because both of us have no experience with it and I care rather more (and as you and I have discussed, thistleingrey, I tend to do all the social management as well), but I suspect a large degree of that is cultural as well. In the cultures I'm a large part of, it's almost always the woman who is "supposed" to do those things, and women socialization built around that assumption, so there's a large amount of social inertia against not doing it that way.

(thistleingrey, according to my parents Korea is a wasteland of gender inequality. I'm glad to hear their experiences are very outdated at this point :) )