My dh did this a lot. Every perceived criticism would see him sulking or acting aggressively as a defense.
we’ve been married 24 years, kids are 18 and 20. This is relevant because he really improved (hence still being together) when we got past the stressful child and teen-rearing stages.
he now apologises. Not immediately but he does. He never sulks any more, if he’s angry he can articulate why, which diffuses it. He had the most appalling relationship with his father and his mother left him and his dad when he was a young child, so in my opinion he had to learn that it’s ok to be angry, and that it doesn’t mean you’ll be hit, or abandoned.
if you can be bothered to wait, or to work at it, because there’s no reason why you should have to (I chose to stay because I he was, ultimately, a good father) I’d recommend a really good talk about mutual respect (when you’re both calm etc) patience, love, (again, only if he’s worth it) and sympathy. Sulking is an attempt to control - it’s sad he hasn’t a healthier way to show he’s pissed off.
I wish it hadn’t taken my dh almost 50 years to learn that it’s legitimate to be angry and to express it without sulking, but it did. I’m glad we (I) stuck at it though because our relationship is worth it and we really connect in almost every other way.
good luck.