I can imagine it's tough with him in the house. I think it's great that you are recognizing your own behaviors and reactions that you want to change. It sounds like you still have a lot of expectations from him
Imagine how you would speak to him if he were a roommate or neighbor. You wouldn't take it as a personal affront that he skipped breakfast-- because you likely wouldn't have been making it for him. And you wouldn't have brought it up later.
Something my coach told me that I thought was great advice was to ask myself if my actions are more likely to draw him closer or push him away? It seems like you are doing a lot of pushing.
Can I ask how you feel like a doormat? It's an honest question that I think is worth exploring. I think it's great you responded to him attempt at getting past the conflict. Perhaps wanting to go for a walk with you was another attempt at that-- you weren't ready for it. And he tried again! I see a bunch of positives. Can you see them too?
It sounds like he wants a bit of space and less expectations/pressure... can you give him that?