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Star Trek VI: The Undiscovered Country (1991) More at IMDbPro »

US President Richard Nixon (in office from 1969 to 1974) was known for his firm anti-communist politics. When Communist states China and the Soviet Union broke up their alliance in the sixties, Nixon perceived this as a perfect opportunity to gain an advantage in the Cold War against the Soviets, by improving relations with China. The visit was controversial, because China was at that time considered to be an enemy state. Paradoxically, this made President Nixon the appropriate person to visit Communist China, because he was clearly an antagonist to their government. Had it been a more moderate politician, then this person could have been blamed for having too much sympathy for the Chinese, or not serving the United States' best interest in negotiations.

Spock alludes to this fact, because James T. Kirk is the main Klingon adversary in the Federation, so they know that he will not let the Klingons off the hook easily during negotiations. They can safely send him to eliminate all suspicions of fraternizing with an enemy. It is also another reference to the Cold War, of which there are many in this film.