Most men will have grown up observing their mothers doing the bulk if not all of the domestic work. That is their mental “template” for division of labour in a household.
They may not actively think this is a “woman’s job”, but they will subconsciously expect it to fall into the woman’s scope of work, so they don’t proactively initiate it until asked to do it.
Increasingly younger men are happy to do their share when it’s pointed out to them. Very few men under the age of 40 would actually say “I am not doing that, it’s her job.” It just doesn’t occur to them to do it themselves.
My DP, who is generally happy to pull his weight at home and does a lot of cleaning / shopping etc wasn’t so hot on the mental planning aspect. He got into a bad habit of saying: “Have you done x/you need to do x”. It was just his default setting. I sat him down and said “stop assuming that all of this is my wheelhouse. You are perfectly capable of doing this/booking it yourself.”
He was completely nonplussed by this: he said he thought I preferred to do it. I I told him I was tired of having to project manage everything in the home and he needed to step up and do a bit more anticipating and take responsibility for the output: ie if you can tell me the cats need worming you are capable of going into the vet and getting the treatment. I work full time and It’s not always up to me to direct what you do.
To his credit he has stepped up. But it was a real eye opener for me. I think a lot of these men (not the total cavemen but the slightly less proactive ones) have internalized the idea that while they have a duty to “help”, it’s still up to the woman to direct all of this.
Hopefully the new generation will be a bit better.