How did the Cuban Missile Crisis lead to better relations between the United States and the Soviet Union as detente was established?
To the extent that the Cuban Missile Crisis actually led to better relations between the United States and the Soviet Union, it was because both sides were alarmed by how close they had gotten to all-out war when neither side really wanted that to happen in the first place.
In the crisis, neither country was actually intending to go to war with the other. However, the lack of communication between the two and the lack of understanding of their respective intentions caused the crisis to escalate. In the wake of this near disaster, the two countries created ways to communicate and tried to dial back the rhetoric that had helped lead to the crisis. In this way, the Crisis led to better relations and communications because both countries wanted to avoid future situations that might escalate.