> The point of good argument isn't to convince the other party they are woefully wrong and everyone should just eventually come to the same conclusion.
Applied to both parties in the argument, yes it is. Argument is digging for truth. The most productive outcome is for some or all of the parties involved shift their beliefs to more accurately reflect reality.
Just to clarify - when you argue, are you attempting to present the actual reasons you believe your point to be true? If not, then you are arguing in bad faith, and contributing heat to the discussion rather than light. If you really are arguing in good faith, then it's just plain crazy to strengthen your position upon being confronted with flaws in your reasoning.
> Some debate for sport/fun
In the context of a serious discussion, I believe the term for this is "trolling".