I need advice... my husband is extremely sensitive...

My husband and I have been married for almost 4 years. He is a good man, hardworking, caring, but he is extremely sensitive and I feel like every day it’s just worse. He used to not be like this. He takes every little thing to heart and gets upset. I can say something as simple as “hey can you take out the trash?” and he will respond with “I guess I don’t do enough around here, eh?” Or another example is, this morning I woke up in a bad mood because our 1 year old kept me up most of the night. I was quiet during breakfast and he was like “are you mad at me? You’re always mad at me.” And I was like “no I just don’t feel that great today.” But instead of doing ANYTHING to make me feel better, he has be silent all day, moping around, literally sulking around the house like a depressed teenager. I feel like I have to fake being in a good mood 24/7 because he seems like he cannot function unless I am happy-go-lucky constantly. I cannot express any emotion other than happiness with him otherwise he makes it all about him and makes me feel guilty for it. If I try to discuss any type of issue with him, he gets so depressed and upset about it that I have to stop and lie and say something like “never mind, it’s okay” and fucking comfort him. I am so exhausted from this. I have spoken to him about seeing a therapist but he refuses, he doesn’t “believe” in psychology and thinks it’s all “nonsense”. So I feel like I’m just going to be trapped in this existence where I fake being in a good mood all the time so I don’t have to deal with him moping around acting like his puppy died. What can I do?

Also- yes I’ve tried to discuss this with him. The end result is the same, he gets extremely upset and just guilt trips me about it.