Well, if you can't produce any evidence that it's evolution that means I should do the housework, then I don't see why I should produce any that it's nurture!
And since you quite rightly state that it makes no sense for men to be better mechanics, because cars didn't exist, it make similarly no sense for women to be naturally better house-keepers, as houses, hoovers etc. didn't exist. Therefore, it must be nurture no?
As to childcare - you are mixing up people who normally do it, historically, with whether they are better at it. Empirical evidence please that women are better childcarers (not just the default, but measurably better at raising children), or again, it can't be nature and therefore must be nurture.
Finally - I've lead a sheltered, geeky life, yet I don't have enough fingers to count the unwanted contact I've had from strange men in pubs, on the street, and even in the supermarket! Every woman of my acquaintance has had similar experiences. Perhaps we live in very different circles.