I can't think straight now. Proving you are right can wait until the other person feels calmer. To establish some common ground, find something you and the other person can agree on. I wasn't home last night. So I couldn't have gone to the movies with you even if you had asked me.
Appropriate humor can ease the tension, but never joke about the other person's feelings or needs.
Admit when you are wrong. An apology can end a conflict. Keep your distance, use a calm voice, and avoid aggressive gestures. Speak slowly and quietly, without blaming or accusing. Recommend doing something to relieve the stress.