I have been through something similar. Now, aside from the question of whether you should go to counseling - the answer is YES! - I will respond to your question about how to explain it to your husband. But please, get counseling whether or not he ends up understanding.
It has to do with respecting each other as unique individuals. Just as he may not see the need for you to talk with a professional counselor instead of just family members, he may not understand why you like/dislike certain foods. He might love mushrooms, but you can't stand them. That doesn't mean he is "right" to like mushrooms or you are "wrong" to dislike them, it means that you have different responses to mushrooms. Mushrooms on a hamburger might make him very happy, but would have the opposite effect on you. In the same way, talking to family might very well be exactly the kind of support that he needs. But family support alone is not working for you. Doesn't mean he is right or you are wrong. Just that you are unique, one of a kind individuals - and that's why he loves you, because you are YOU and not a carbon copy of him!
I have had similar discussons with my husband in which I would express a need and after I explained what I needed and why he would say, "Well, I just don't undersand why you need xyz, why can't you just abc?" The response to this is "It's okay that you don't understand. You don't have to understand, you just have to trust that I'm telling you the truth when I say I need this."
Finally, one explanation that might help him understand, even though understanding is not required for him to be supportive, is this: When you unload on family members, whatever was said stays in the relationship for years. If something was said in anger, or while hurting, it can hurt the relationship. If you're one of those people who thinks more clearly out loud, if you're talking to someone who you care about, you're going to do a lot of self-censoring and be more focused on how they will react to what you're saying, and that takes focus away from figuring out what you really think and feel. When you're talking to a counselor, you're in a neutral space, paying for their time, and so you feel freer to say what's really on your mind which is the first step towards figuring out how to move past it.