Hi OP, I hope you're feeling okay today.
The fundamental issue here is that you both have different ideas of what equality should mean within this relationship.
You believe that it should be equal reciprocating of gestures and spending. He believes it's measured on some sort of point system.
You need to address this, for what it is and not for what it is in one moment. Losing your temper at one instance doesn't make him see the big picture, it gives him something to hold on to and excuse.
Instead of specific "I did this and you did that on these dates" try "I feel as though we should aim to -very specific goal here-". Then you are able to both get your points across without harping back to the past and never moving forward.
You've bitten your tongue in what you feel is an unfair situation and it's gotten away from you, continued too long and built up inside you.
Also, he's a douche.
I would recommend to go forward with something along the lines of this:
Thank you for agreeing to give me time to process things. I appreciate that you are unhappy discussing the subject further, however I feel it is something that absolutely needs to be talked about.
I feel as though our relationship hasn't been very equal, despite this being what we both want.
I understand that my home situation means that it makes more sense for me to come to you, and I have no issue with doing this. However, when I come to you I don't feel as though I am a guest in your home. (State your reasons for this, labeling them as your feelings and not his actions).
Go on to explain to him how the situation is different when he comes to yours and how you are happy to provide food and beverages for him when there. And would like to see yourself treated the same way.
Again, keep the language free of blame.
Where you absolutely should be firm is where he talks about how he works harder than you etc.
Explain to him that you don't feel respected when he talks to you that way, and you feel as though he doesn't feel his time is as valuable as his.
Explain that there is a difference in your income and that it's not easy for you to provide for both your household and his, and suggests that maybe he hasn't considered this before, because he earns more.
Explain that your relationship has been able to progress because you have gone to him and that he's not "putting you up" but doing his part to make things work, as you are.
Put forward a suggestion that you both maintain financial independence if it's so important to him to be equal. Pay your part for your meals, bring food for yourself alone when you go to eachothers homes.
When he tells you that's ridiculous, which most people would, suggest he treats you like a partner then and stops keeping score or doesn't treat you like anything because you're worth more than this.
Sorry I think I've just gotten away with myself 😂
I was in a relationship with a guy a while ago. We lived together, we shared the bills. He earned more than I did but insisted everything was 50/50. But he would never pay for any treats. It was always on me. Which was fine. I was broke and he had steady savings. After a while I stopped including him in treats. I would take myself and DS out for food or to the cinema and not include him. And he would complain. I explained that I couldn't afford it all on my own and that he would have to start being 50/50 away from the bills too or just miss out.
...we didn't last long. Some people are just dicks.
Good luck OP