"The" wife at one time was considered a lower-class, working-class, blue collar way to put it.
I on the other hand have always used "the" because it avoids the ownership suggestion of "my," as if the individual is a slave.
Just as I've always said "the" secretary or "the" attorney or "the" physician, rather than my, my, my, because I don't own these people and "my" is especially demeaning to the secretary.
I've noticed that Democrats, liberals, and primitives invariably use "my" more than decent and civilized people do, probably a leftover from their slaveholding days.