I read this, the whole time thinking "please don't make a cooking or cleaning analogy", no such luck.
The conversation wasn't nearly what I expected, it goes into more detail than I expected but there are a few points, like the sweeper thing, that were probably big triggers.
It took years before I referred to my wife as anything but "my wife" even at work, because most people didn't know her, and so didn't know here name and it was simply easier to refer to her that way.
At this duty station I'm the same. No one here knows my wife so I don't refer to her (or even my children) by name.
At my first duty station it was much more tight-knit; we knew each other by first name, met off-hours as a group (including spouse and children), etc. So there it wasn't unusual to refer to someone's wife by first name.
Now I can see why people would be offended about referring to "the wife" (and it's less savory alternates), as if you were resigned to torturing yourself once you got home and not actually in a committed relationship with a human being. But that's not what is happening when talking about your actual wife, just as it's considered perfectly acceptable to refer to one's mother, brother, father, or sister by role instead of name.
She's his wife, that's personally identifiable information by itself, far more so than a first name. Also I assume that he ran it by her first in any case as to post that conversation without clearing it with her would be a very bad move. I rarely post anything to do with my wife online and never without talking to her about it. There is also a large difference between vocal habits and written habits. I feel like replacing wife with a first name(even a fake one if she didn't want her real one posted) would have been less likely to offend. (I assume it was his intention not to offend as he removed the piece due to it offending)
The conversation wasn't nearly what I expected, it goes into more detail than I expected but there are a few points, like the sweeper thing, that were probably big triggers.