My own experiences make me suspicious of the underlying assumption that people are telling the truth about division of labor.
I do the cooking, all of the dishes, trash, yard work, and vacuuming. I also pick the kids up from school every day and help them with their homework. My wife does laundry and occasionally cleans a bathroom. Yet if you were to ask her, she does the lions share of the housework. She's not intentionally lying either--she really believes it.
That matches my own experience and it seems to be cultural. In a household where the man normally cooks, the question as to who usually cooks might typically be answered in three ways:
Scandinavian lady: "He normally does the cooking." No need for excuses as no judgement is attached.
American lady: "He likes to cook so he ofter does it, to relax after work." Feels the need to excuse it so that she is not an evil scorpion ***** wife from hell.
British lady: "I always cook, you could not trust him in the kitchen"
I remember reading a story in Denmark about research that showed the Scandinavians were unusual in only slightly exaggerating what they did proportionately. I have also read that while women grossly overestimate the time they spend on housework and work they also slightly overestimate the amount their partner does, men tend to underestimate both what they are their partner does.
And all three will be sincere. I suspect in a house where the man is doing almost all of the housework and working hard at work, it will be reported as splitting the housework about evenly and he might well lose patience.
I also had the acquaintance of a lady who left her husband who consistently and willfully earnt less money that her (there were other reasons too). She felt shallow for letting it bother her, and he had tried to compensate by doing most of the housework. Considering that he was a poet who wrote about feelings, that was brutally insensitive of him.