The general rule is while I'm in school, I cook for us both and my boyfriend does the dishes, when I'm on break I cook and do the dishes. So, it's finals time, and he get a cute pout and asks if I'll do the dishes this time. I told him "if I get a chance to I'll help., but I'll probably be busy all day" Fast forward to later, this afternoon, where I'm doing homework and getting ideas written down getting ready to shoot for one of my finals. He asks "now tell me again why you can't do the dishes today?" I'm assuming he thought I was goofing around online rather than working on homework, so I told him I was doing homework and can't. Mind you, he's playing Metal Gear Solid 3 this whole conversation. He gets mad, doesn't say anything, but I know that look. A little while passes, I finish up on the computer and am ready to shoot. He breaks his silence to point out that the two characters on screen are gay, I giggle and go to give him a hug. He sits there and takes it, but doesn't really reciprocate. He then says "I'm still mad you won't take a 20 min break to do the dishes." I really wanted to say "I should take 20 minutes from doing my homework to do them so you don't have to take 20 minutes from playing a video game to do them? Seems fair..." because I didn't really want to start anything.
Eventually, my camera battery dies, and my extra seems to have lost its charge since it's been forever since I've been able to shoot digital for an assignment. So I tell him "you got your wish, I have to take a break and let my batteries charge."

Dishes are a problem a good part of the time. Between hours spent IN class, and twice as many hour spent outside class working on assignments, lately I'm only ever home to cook (him dinner before he goes to work, which often means coming home early just to have that done in time) and sleep. He feels like since he works full time and pays rent/electric, it shouldn't be his job to clean up the dishes I dirty. He won't cook because he never learned how (and is stubborn as hell when I try to teach him). He tried making himself grilled cheese while I was in class one day. Let's just say it was a disaster.
I don't mind cooking for him, I always loved experimenting with food when I was younger (I've taken nearly a half hour to make THE PERFECT MEAL-SIZED SALAD but oh god it was so good). I just need to find a way to deal with the dishes issue.
Anyone ever have a similar problem in a relationship? How did you handle things?

Oh, relationship info: dating 3 years, living together for most of it, getting engaged when money isn't so tight, we're awesome.