Why is the fact that the Americans are helping the Russians important?

In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is important because avoiding a nuclear war is of paramount importance.
In Clancy’s story, the Americans are put in the awkward position of having to help Captain Marko Ramius in his efforts to defect to the United States with his nuclear-powered ballistic missile submarine and having to help the Soviet Union to “find” the highly-secret submarine—in order to avoid a panicked reaction against the United States. The Hunt for Red October was written during a period of intense and extraordinarily dangerous relations between the United States and the Soviet Union. The early-1980s were characterized by a large build-up in American military capabilities after a period of degradation. Modernization of American nuclear forces was a very prominent component of that build-up. In addition, both sides were adept at carrying out sophisticated naval operations intended to both collect intelligence on the other side while enabling ship and submarine crews to prepare for an actual war—a war that thankfully never materialized. Submarines and anti-submarine warfare were among the most secretive elements of the military competition between the two superpowers, and Clancy’s novel accurately captured the technological intricacies and political machinations that played out daily in the world’s oceans and seas.
The United States, under the circumstances depicted in The Hunt for Red October, helped Captain Ramius because the Navy and intelligence community desperately wanted to know as much as possible about Soviet submarine design and construction: the Red October represented the pinnacle of Soviet engineering. In addition to the intelligence that could be gleaned from examining the submarine firsthand, enormously valuable information could be conveyed by Captain Ramius after his arrival in the United States. As Admiral Greer points out at one point regarding the Soviet naval officer, "He's about the best sub driver they have, a real charger.” Captain Ramius could provide the West with invaluable insights into the thought processes of the Soviet Navy, as well as information on Soviet naval tactics. In short, the Americans had powerful incentives to help the defecting Soviet officers aboard the Red October.
The more important question regards the decision to help the Soviet government track its missing submarine. Here is where Cold War machinations and intelligence-gathering methodologies come into play. Until Ryan can convince his superiors, all the way up to the presidency, that Captain Ramius is a genuine defector, the United States must cooperate with the Soviet Union in locating the Red October so that it can be captured or destroyed before it is able to launch an attack on the United States. It is, in short, in both sides’ interests that the submarine be located and neutralized.  As Ryan notes in his meeting with the president,

The SS-N-20 has a range of six thousand miles. That means he could have hit any target in the Northern Hemisphere from the moment he left the dock. He's had six days to do that, but he has not fired. Moreover, if he had threatened to launch his birds, he would have to consider the possibility that the Soviets would enlist our assistance to locate and sink him.

Once the American government becomes convinced, however, courtesy of Ryan’s persuasiveness, that Captain Ramius is defecting and is not a rogue officer intent on starting a war, the United States still must be seen cooperating with the Soviet Union to enable the surreptitious capture of the submarine and its commanding officers without the Soviets knowing it has succeeded. This requires a deft touch; the Navy has to be perceived as helping the Soviet Union while simultaneously conspiring against it.
American assistance to the Soviet Union is significant because it is considered mutually advantageous and because it is part of a ruse to secure possession of the submarine without the Soviets knowing it.