So men and women are exactly the same and do everything exactly the same way? 

There are differences that are natural to each of the sexes.  It doesn't mean that a man is never nurturing or a women is never seeking status.  But you jumped on what I said before I explained myself, which I was going to maybe do in another post.

The solving the problem is realizing what the differences are and then changing our own behavior accordingly.  One can never change anyone else.

Example:  A lot of time I get upset with how the men talk to each other on CathInfo.  I realized it didn't bother the men all that much, so I was trying to understand why.  Many times I feel (I know feelings aren't really allowed here) misjudged by my posts, and I wondered why the women tended to understand better and I felt the men were accusing me of being sanctominous, or a Karen. This is why my son came up with this nurture vs status and I thought it was great, so I wanted to talk about it.  He hasn't read Men are from Mars and Women are from Venus.

Again my post was focused on helping others understand (nurturing), yet some how it was changed into Pop physchology.  Because of modernism and the lack of church guidance, we no longer have this information passed from generation to generation.  So before you quick judge my meaning, please wait for the other post.  I don't want to have this conversation here.  I am sorry I felt the need to explain myself.
And that does not happens in all households, some men are just completely oblivious.

We both cook, clean, do dishes, and get the kids to help as well.  Not sure who does more or less between us, we haven't really kept score.  Of course, we both love to cook, so generally it is a thank you we do for the one who prepared the meal to do the dishes for them.  And out of courtesy to the ones who will be doing dishes, the cook tries to wash as the cook. 

As a man, I think it is important for boys to see me doing dishes, as they ought not be slobs when they leave the house on their own, and to learn other skills and virtues.

I'm a husband and I grew up with a small family restaurant. One of my tasks as a young boy was to do dishes for the restaurant, sweep and mop, etc. which I also did at home. Now many years later I still do the dishes, not because my wife demands it or anything like that but because I find it soothing and relaxing. That may seem strange to some but while doing dishes I am looking out the window and seeing nature, bird baths and feeders full of life and it gives me a sliver of time when I can just think and reflect on something. No pressure for creativity... just me and the dishes with a very predictable process and outcome.