So, in other words, whoever has higher standards for cleanliness or whatever issue you'd care to discuss, should be the one to set the agenda, and define what compromise means.
If I want some mess, and she wants no mess, I should compromise what I want and start scrubbing floors? And this is equal how?
Let's take another issue as an example.
Let's say I want to be monogamous and she wants multiple partners. Is it the function of an equal relationship to ensure that she gets her way? Or should she sacrifice her desires to satisfy my preference?