Lernaean

For the sake of this discussion, suppose you are a moral relativist. That is, suppose you don't believe that any moral laws, known or unknown, are true, correct, objective, or whatever label you prefer. 

With that in mind, I've had some trouble recently reconciling my moral relativism with my ability to discuss moral issues with other people. I have a personal moral code that I try to live by, but I fully believe that it entirely subjective and no more "correct" than anyone else's. I frequently hear other people talking about moral issues and their views on them, and I often find that I disagree with them. I want to have a conversation with them about it but I don't know how to properly do it.

How is one supposed to have a meaningful discussion about right and wrong with someone else if you fundamentally don't believe right and wrong objectively exist? It feels like I am essentially saying, "You should believe in my moral rules because I want you to." One can make these arguments from a pragmatic or compassionate or whatever standpoint, but valuing those standpoints still seems entirely arbitrary. 

Has anyone else struggled with this issue or otherwise see a way of dealing with it? I enjoy having moral discussions with others, but I don't like feeling like some sort of hypocrite or fraud.