OP - your husband's reaction is telling.
It is a classic over reaction.
Oh I won't talk to ANYONE EVER - is disproportionately defensive.
I'd hazard a guess he was enjoying the flirting and feels guilty and cross that you've called him on it.
^^ absolutely this x 1000.
Either he feels caught out and a bit stupid, or you've ruined his fun. But he was feeding it and he knows it.
Don't let him make you feel bad Op. if he brings up the subject again, put him in your position and to ask him how he'd feel. The extreme reaction is ridiculous. He sounds like a petulant child. But ok, he never speaks to anyone ever. Just say "ok, if that's what YOU want. I just wanted a little more respect on a public forum, but if YOU feel that way then YOU have made that decision".
Don't let him push guilt onto you.
Or ignore his sulking until he grows up.
My stbxh never apologised and used to wait for me to cave in to keep the peace. My patience ran out eventually.