Why did the u. s. senate reject the treaty of versailles?

It's mainly because of Article X of the Treaty, which required members of the League of Nations to come to the aid of other nations in the League when they were attacked.

Many senators, led by Henry Cabot Lodge (chair of the Senate Foreign Relations Committee), worried that this provision of the treaty would drag the United States into unnecessary foreign conflict and thus impede on America's freedom of action. Hence, they wanted to ratify the treaty with "reservations" (known as the Lodge Reservations) stating the United States would not be obligated to intervene should a member nation of the League of Nations be attacked. There was also a faction of U.S. senators called the "incorrigibles", who wouldn't accept the treaty under any circumstances.

Woodrow Wilson had essentially given up all of his famous "Fourteen Points" at the bargaining table at Versailles with the exception of the creation of a League of Nations. Therefore, he refused to compromise. It didn't help that just as Wilson was about to go on a huge speaking tour across the country in favor of the treaty, he had a crippling stroke. So the Lodge faction and the incorrigibles formed a big enough voting bloc to ensure the defeat of the treaty in the Senate.