Suggested improvements to use of Party / Counter-Party

Use of PartyID-CounterPartyID - why do we need both in a single payload? Wouldn't a given party know what its own ID is? So in the context of any given interaction we simply need to know the partyID of the other party? If we respond to something from a party, do we not simply pass our partyID to the counterparty since they know who they are, they just need to confirm who we are? (in addition to the other transaction identifying information?)

The analogy is Bob and John have a conversation:

Hi Bob, this is John, how are you today?

Hi John, this is Bob, I am fine. (Duh - I know you are Bob, I just asked you a question and identified you in the process. Assuming there is some sort of discovery process I already know he is and why I had his identification before I even talked to him)