My old boss used to refer to "the wife" and the way he meant it, it sounded like she was the authority figure that he had to check with to do something. I thought it was derogatory and insulting the way he said it and I'm sure he thought he was being cute with the the guys.
"My wife " does sound like a possession but I can understand someone using the term "my wife" when talking to someone who doesn't know her and doesn't want to get personal with a stranger. I have also heard many women who used "my husband' as a non- personal type statement to someone they don't know. To someone who does know her, them he should use her name.
IMHO - In a non-personal situation, a better term would be to use "my spouse", indicating that you are equal partners in life and share what you have together but then, what do I know, I'm single.
