Me and DH had an argument last night about this. He referred to me as "my woman", it was just in a conversation between us and not public. But it gave me the ick immediately and I politely asked him not to refer to me like that again.
He got in a huff and couldn't see the issue, rationalising there's a difference between "my woman" and "my wife", which I'm fine with.
IMO, there is a bih difference. It's not only grammatically incorrect, I find it feels possessive and old fashioned. I'm not an object to be owned.
I realise this is very much a first world problem. But it's disrespectful, right? If I don't like something - within reason - then just don't do it. Why argue? Or AIBU and overly sensitive?