> Why doesn't the husband notice that his wife is always picking up after him, or that she is not recieving acknowledgement of the work she has done, work that he feels should be acknowledged when he does it?
Blind spots of attention. When she does it, the (unconscious) reaction would be "I didn't need it, I'd be fine either way". When he does it, the (unconscious) reaction would be "I didn't need it, so I wouldn't do it, but I did anyway".
> Why must the woman be the one to notice there is a problem,
It's not that woman must notice a problem, it's that woman did notice it.
> [...] to [do all the work with problem], as if the problem is her problem to solve and not a problem with the relationship, which consists of two people who are supposed to be partners?
Again, it's the attention and its blind spots. The problem didn't get noticed and acknowledged as such in the mind of man.
If you want me to do something, it's you who normally should put effort, not me, because I don't care if you will have it done or not. This is how interaction between two people works. It's silly to expect me to look around for the ways to please you out of the blue. Why would you suddenly expect this mechanics to work differetnly in a relationship?
--
[Clarification]: The description above is about how things work between people, not a praise of man's passiveness. If a couple wants to change how this mechanics, they need to put continuous effort in working against it, and this means they need to notice it and decide to do so.