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Step 1
Find neutral ground that you and your opponent can agree on, even if you haven't reached a final resolution on the issue. Even if it's the tried-and-true decision to agree to disagree, both of you can walk away feeling like you saw eye to eye on some aspect of the fight and neither of you lost.
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Step 2
Reiterate your stance when you bring the fight to its conclusion because ending the fight doesn't mean you're giving up. This allows you to convey that you haven't changed your mind without antagonizing the other person into further arguing.
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Step 3
Be understanding of the other person's viewpoint. Give credit to your opponent's opinion so that she will be willing to end the fight without feeling slighted. If you refuse to budge at all, she will just want to keep fighting. If she feels that you have some understanding of her side of the issue, she will be more willing to end the fight quickly.
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Step 4
Ask to end the fight politely. There's no need to be rude or abrupt when ending the fight; this will only make the situation more negative and antagonistic. Explain that the given time or place isn't appropriate for such a heated debate and request that the two of you discuss the matter elsewhere. This will make you look polite and respectful while still allowing you to end the fight efficiently.
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Step 5
Establish a time to talk again. If you and your opponent both feel that the issue is still unresolved, end the fight on the grounds that the two of you will meet again soon and discuss the issue more calmly. This guarantees that the problem will be fixed in the near future and still end the fight for the time being.
