One of the main reasons why President Nixon decided to try to improve relations with China was because he wanted to improve relations with the Soviet Union. This happened in the context of the Cold War.
The Cold War was a conflict between the Soviet Union and the United States, along with the countries' respective allies. The Cold War was not an armed conflict; it was a conflict of ideologies. The Soviet Union supported communism, as did China, which led to the two countries becoming allies. Nixon hoped that by fixing the relations with one country, he would be able to improve relations with both.