Question

which nation rejected the Treaty of Versailles, negotiating its own peace agreement with Germany in 1921

Answer 1

You might be surprised -- it was the United States.

The Treaty's approval was blocked by a Senate leery of the condition set within it that asked for aid if any nation within the League of Nations was attacked. Senators were worried that the obligation would override the US' sovereign right to decide when and where they would go to war and tie them up in another foreign battlefield.

The Treaty was signed by everyone else, but the US got a separate one with Germany without the hang ups of the Versailles treaty.