Hmm, it seems to me that people where living together in some sort of loving union before any Christian religion defined the term marriage.

Yes, and when it was a union recognised by the local state/religion, it was almost always (with a few exceptions) male-female. Furthermore while yes, loving unions existed, Judiasim (which Christianity branched off from) set aside a specific kind of loving union and called in marriage. Thus it belongs to the Jews and to us by inhearitance. I suppose the Jews could say we can't use it, but they haven't, mainly, I think, because we use about the same definition for it that they do.