Senator Henry Cabot Lodge did claim to object to Article 10 of the Treaty of Versailles, claiming that it would drag the United States into another future war in Europe, this time defending one of the League of Nations' countries that happened to be attacked. While the idea of the clause was collective security (strength in numbers), same as the future NATO alliance was built around, Lodge argued to a war-weary America and Senate that to sign up for such an obligation was foolish.
In reality, it is important to remember that Lodge wasn't necessarily arguing this because he believed the point so much as he just wanted to hand his political enemies: President Woodrow Wilson and his fellow Democrats, a big defeat right before the 1920 election to decide his replacement. Politics like this has been around a very long time.
Lodge's primary objection to the League of Nations would be that it would handcuff the ability of the United States to be an active participant in its own foreign affairs. The concept of an international organization scared Lodge because it essentially took away US autonomy, embroiling itself in the conflicts in Europe:
We shall make mistakes in the future and fall short of our own best hopes. But none the less is there any country today on the face of the earth which can compare with this in ordered liberty, in peace, and in the largest freedom? I feel that I can say this without being accused of undue boastfulness, for it is the simple fact, and in making this treaty and taking on these obligations all that we do is in a spirit of unselfishness and in a desire for the good of mankind.
Lodge argues that another part of the problem with such a design is that it limits the United States in dealing with European nations, whom Lodge feels have different agendas and political aspirations. Each one must be viewed on an individual basis. To view them all in the same way, without any distinction, is a recipe for disaster, according to Lodge: "But it is well to remember that we are dealing with nations every one of which has a direct individual interest to serve, and there is grave danger in an unshared idealism." Finally, I think that Lodge believed in a "United States, first, all else second, mentality." He was not persuaded by Wilson's claim that it's the nation's role to be the watchdog of the world, nor that the League was actually needed for peace. Lodge felt that US entry into to the League would be maniuplated by other nations, who would get along fine without the US presence: "We are told that we shall 'break the heart of the world' if we do not take this league just as it stands. I fear that the hearts of the vast majority of mankind would beat on strongly and steadily and without any quickening if the league were to perish altogether." In the end, these reasons end up compelling Lodge to reject the concept of the League of Nations.