I agree that most people define the word “relationship” in the way that you do. I suppose, for that reason, that I prefer the word connection. That word does not imply anything casual for me. I am more than a piece of meat. I can be as deeply connected as in any “relationship.” The only difference is that I choose not to wall off or to control another person, thus allowing her to enjoy whatever life presents. The only reason that I can fathom for demanding monogamy of another person is for the sake of ego and of self-interest.