Men are from Mars, Women are from Venus has some great advice about how to ask/get men to do chores. For example, you might be phrasing it in a way that that is counterproductive. There is a big difference to most men between the words like "can" and "could" compared to "will" and "would". If you're asking him if he "can" clean the kitchen he might be subconsciously understanding it as you asking him if he is physically capable of cleaning the kitchen. I know this might sound like a giant eye roll, but a lot of men are literal like this. You don't really mean to ask if he "can" do something, so switch it to "will."

Also, appreciation can go a long way to ensure repeat behavior, for anyone. Imagine if he was enthusiastically grateful to you every time you did a chore. Chores might not be so annoying to you then. Same goes for him. Try genuinely thanking him the next time he does anything, like wash his own plate, or put any piece of clothing away. It'll probably make him feel good and make him want to do more, because being thanked feels good.

It might sound stupid to thank someone for doing what you think they should already be doing, but it works. It feels good to be thanked and honestly it feels good to be thankful. People start to sound nagging when they repeatedly demand things be done instead of asking if someone will do something. I agree that chores should be split and it would be amazing if both partners had a clear idea of who needed to do what and when, but that's rarely the case. If you want him do to stuff you have to start speaking his language.

The book also talks about how to respond when you ask someone to do something and they groan and complain. You straight up ignore it, assuming it's not a valid response to your question like they have a deadline and need to finish something in time. But things like "ugggh.. mannnn" just get ignored. You'll never get him to want to throw his trash away. If groaning bothers you think of it as the audible process of him switching his train of thought to focus on whatever you asked him to do. Stand firm in your question. If he tries to pass it off by saying something like, "can't you?" Respond with a short, "I'm already doing ___." Then don't say anything else. You'll open it to an argument if you let him distract the point.

It used to be really hard to get my boyfriend to help out with chores. So one evening, after reading the book, I asked him if he would take the garbage out to the curb since it was supposed to get collected in the morning. He said ok, then later when I saw that he had done it I went up to him and genuinely thanked him for doing that so I didn't have to in the morning, and that it made me really happy. After saying that he stood up a little taller and said, "tomorrow morning all take out the recycling too!" It was all I could do not to burst out laughing, but I knew he was looking for more thanks so I told him that would be amazing!

I hope that helps because I totally feel you, that's a frustrating situation to be in.