Particularly in political debates or elections, one party can withdraw without necessarily conceding defeat.
Further on that topic, if the party were to withdraw from the debate at a point when both parties are on equal footing - neither winning nor losing - the party that withdraws may appear weak to observing parties.
However, if the party were to withdraw at a point where they are clearly winning, and the opposition party is no longer making even remotely valid points, it would not appear weak to observing parties. Depending on context, it may appear mature, arrogant or funny, to name just a few possibilities.
Withdraw - cease to participate in an activity
You could cease and desist from further communication.
This would imply a formal and very serious tone.
You could discontinue the argument.
This lacks finality and could be used if you might want to continue it later. Also, quite neutral.
You could (refrain/restrain yourself) from further discussion.
This may have good applicability to the OPs specific circumstances. Implying you want to continue arguing your point, but you need to stop yourself.
You could forgo further discussion.
This could imply you want to keep debating but for some reason you can't, maybe because you're running out of time. Also quite a polite way to end a discussion.
In a different tone, perhaps to keep the peace:
You could contain the argument.
Keep it from straying where it shouldn't.
You could suppress the argument.
If you're Dr. Evil and they're about to publicise your plan for world domination.