How did Wilson's refusal to compromise doom the Treaty of Versailles?
I assume that you are asking about Wilson's refusal to compromise with such opponents of the League of Nations as Henry Cabot Lodge. If so, Wilson's refusal doomed the treaty in the US Senate because it caused Senators to have to choose between Wilson's way or nothing. Many Senators would have been willing to vote for the treaty if it had had a few modifications. But Wilson rejected any changes, insisting that the treaty had to passed exactly as he submitted it. This led to a situation where he encouraged Senators to vote against the treaty because his opponents had attached conditions to it.