What argument did the Senators who opposed joining the League of Nations make?

Membership in the League could draw the United States into future wars.

Explanation: There was a clause in the Versailles Treaty (which set up the League) that stated that if Country A is attacked by Country B, and Country A is a member of the League, then all other countries in the League had to help fight Country B. The Senators who opposed joining the League said that this clause would take away Congress's constitutional right to declare war.