It’s never really about the dishes. The dishes are just a thing in physical space. That isn’t to say that you can’t be Disrespectful with dishes or that one or both people’s behavior and expectations regarding the minutia of the kitchen isn’t unreasonable. But fighting about dishes is really good indication that there are more fundamental underlying schisms in the relationship that should be addressed.

In my personal experience both in my own relationships and viewing the relationships of others, I feel like the domestic partner can often feel trapped and/or unfulfilled. It’s easy for the breadwinner to say “I bust my ass all day and I make all the money so that we can have this life”, but the other partner in this arrangement becomes totally at the will of the breadwinner. The breadwinner could change jobs or decide to move or divorce and continue working, but the domestic partner is totally effed. It isn’t an equal partnership unless the domestic partner truly feels agency. And until that point this underlying resentment will come bursting up like new islands in an archipelago, until the situation is resolved or dissolved.

Edit: the sibling comment regarding narcissism is also worth reading! I don't know your situation. Labeling someone as a narcissist is a nuclear option because it means you don't really see them as fully human anymore, but it can be appropriate if you have a large body of evidence.