No good comes from a lack of communication. Even when there is tension in the air, not communicating is not the way to handle it. One of the great things about my wife and I happens during those times when we bump heads. It is not uncommon for one of us to say to the other, "I want us to talk but I need a little bit of time first to calm down and collect my thoughts." (I am paraphrasing here but that is the essence of what is said.) Such a comment is a perfect example of effective communication, particularly during a time when cooler heads are on the verge of giving way to non-cooler ones.
Such a statement is a declaration that it is important for the parties to talk. At the same time, this statement emphasizes several key points: (1) for the conversation to be of the greatest benefit, both parties need to be calm; (2) despite the disagreement, both parties want to return to a more positive place; (3) mutual respect remains very much on the table; and (4) both parties want to be heard but are also willing to hear what the other has to say. It is important to inject here that even with this understanding, it does not mean the conversation that eventually follows will be a totally smooth one or that the parties will not continue to "agree to disagree." At the same time, it does put them on a positive path toward resolving their differences.
The statement where one party asks for a time-out and the other agrees to that request represents a verbal contract where ground-rules have been set. This gives both parties a tangible path for each to follow as they strive to reconcile whatever misunderstanding may have occurred. Without such understanding, whatever communicating that may follow will in all likelihood be more chaotic, off-topic and hurtful. In other words, it will increase the tension rather than take the air out of it. Tension as a result of a disagreement only becomes a relationship-breaker when the parties involved cease to communicate effectively.