Would this make you mad if your partner did this?

Tbh I don’t really know how to feel right now. I’m still kind of pissed by the fight he’s referencing that “I started” last week. I’ll give some background.

Fiancé and I both had long weekends last week and he offered a deal - he does laundry at the laundromat (our dryer died) and folds clothes/puts away, I clean house so we can enjoy days off. After I cleaned, he decided he didn’t want to fold clothes and said I was unreasonable for “picking fight”. His solution was to buy two sided hamper and says we’ll do separate laundry from now on (despite the fact he will throw my clothes on the floor if I have something in the washer when he needs it, instead of putting it in the dryer, or if in the dryer just throw on the floor instead of a basket or telling me they’re done).

He never has helped out regularly, soI do most of it - when he does, it’s a random day here and there when he gets in a cleaning mood. I just feel like this isn’t going to resolve the actual issue, and will only cause more fights. He never ended up folding the clothes or would even admit that he was wrong. I felt tricked and that was the main reason I was upset and did start that fight. He snap chatted me a picture of a new two sided hamper today and was excited about it, but honestly I feel like this is going to cause more fights. I was like, “you really want to do separate laundry?” He responded saying “remember that fight you started last week?” As if this is a punishment for me somehow lol.

He is a first responder, so I try to cut him some slack, but I was before too when we lived separately and I still got my shit done. Also, he does help out in other ways, and I feel like our relationship usually makes up for his lack of cleanliness (and I was always under the impression men are messier anyways). But his whole attitude about this made me really mad, and I found his Snapchat petty. How would you handle this situation?