Which concern resulted in the US Congress rejecting membership in the League of Nations?

American opponents of the League of Nations voiced a number of concerns. But the most important was the potential loss of sovereignty that was widely believed would follow from the United States signing up. In the immediate aftermath of the First World War, a mood of isolationism descended upon the country. It was felt by many that the United States had done its bit during the recent conflict and that it was time for other countries to sort out their own affairs. The League of Nations and all it stood for was clearly out of step with the prevailing mood.
Opponents of the League—and not just die-hard isolationists—argued that it would curtail America's power to develop its own foreign policy in the pursuit of its own interests. They further went to allege that the United States would effectively become subordinate to the League and would end up taking orders from this unelected, international body unanswerable to the American people. There had been a long-standing tradition in American politics of hostility towards "foreign entanglements," as George Washington famously called them, and opponents of the League successfully tapped into that sentiment in putting forward what was ultimately a winning argument.