I'm finding this discussion fascinating, but I'm particularly fascinated by linguistics and language in general.
What I find most interesting is how people are finding each word to be offensive/negative or not for different reasons. For example, some here have said that "the" seems more impersonal and offensive and "my" is more appropriate for denoting the relationship between particular people. While others find "my" to be offensive as if it denotes ownership. Words are so arbitrary, but all of our different cultures and experiences completely shape how we think of words. I also find it interesting that one person commented that they didn't think it really means anything...which is another whole issue--are words just arbitrary things that can have different meanings/contexts/intentions, or are they more powerful regardless of the intention of the speaker?
Also some have noted the ambiguity of using "the" instead of "my," and not knowing whose husband or wife it is, but to me the context of the conversation would indicate the relationship and which particular people to which you are referring, so I don't thing using "my" is necessary for that. But once again, this also depends on your dialect and first language, as many here have noted the different grammars of other languages can influence this understanding of relationships.
I personally think that using "the" instead of "my" can signify importance. When you introduce anything and add "the" to the beginning, it seems to give that person or thing more importance and respect in a way. For example, in my family we often refer to my mom as "the momma," which we use jokingly, but also as a show of respect and love because she is the one and only.