The United States is not a member of the Commonwealth of Nations due to historical and political reasons stemming from its independence from Great Britain in the late 18th century. When the American colonies declared their independence in 1776, they sought to break free from British rule and establish a sovereign nation. This desire for independence was fueled by a growing sentiment against colonialism and the desire for self-governance.
After the Revolutionary War, the United States established itself as a separate entity, developing its own government, laws, and international relationships. While some former British colonies chose to remain part of the Commonwealth and maintain a connection with the British monarchy, the U.S. opted to pursue its own path.
Furthermore, the Commonwealth of Nations is primarily an organization of countries that recognize the British monarch as the head of state, which is fundamentally at odds with the U.S. Constitution and its principles of separation of powers and republicanism. Given these historical decisions and political ideologies, the U.S. has maintained its stance outside of the Commonwealth.