I think the "argument" argument is only raised when people become devoid of an answer. If they have no valid response, the reply becomes, "I don't want to argue with you any more". It was never an argument until one party fails to come up with a valid case...until then it was a discussion.
In that persons mind a robust discussion was interpreted as an argument and a threat to the current point of view to the point where my company was no longer desired.
It happens often on this forum where the word "ignore" is used to say that they no longer want your company in the thread discussion whether or not what you say is valid or not.