I don't think that's true in the general case, maybe in your experience. Someone needs to cook, clean, do laundry, do dishes, take care of babies, etc, and this tends to fall more heavily on women (don't have studies offhand, but this has been researched).

Not to mention that taking care of babies, in some senses, has to be done by women, as men can't breastfeed. (I'm of course only talking about breastfeeding, but it is a significant amount of work that only a woman can do, unless you prefer to feed your baby from bottles, but this has been proven to be less healthy and therefore less preferred for the baby).

I keep on encountering social situations where men are relaxing/socializing and women are running around preparing food. I'm not so sure the gender roles automatically come with an equitable distribution of work, now that technology has eliminated much of the need for the heavier forms of manual labor.

Also, in terms of fixing things, that's supposed to be something you do once, and it stays fixed. Much of traditional "women's work" is recurring.