The word "wife" is as perfectly fine as "husband," no argument there. But in many cultures in the past, and even in some today, the wife has been considered to be a possession of the man, subservient to the man, or both. Gosh, it isn't that long ago that we were saying "I now pronounce you man and wife." And there's a difference between using "my wife" informally, as when your introducing each other to someone ("this is Erica, my wife") and formalising it by typing it, on Mudcat for example. You can then make a slight effort to find a more egalitarian form of words that is difficult to do in informal, casual, spoken contexts. In the latter case, both partners are present, which adds an extra contextual dimension that doesn't happen in print. Makes all the difference.

It's also worth noting that many men make a laudable but clumsy effort to avoid the possessive sense of "my wife" by changing it to "the wife." Some people at least can still see the awkwardness of implying that, somehow, she belongs to you and would rather avoid the allusion, even if you two wouldn't.

She's not called Erica, by the way.