Anti-imperialists were a significant part of American society during the late 19th and early 20th centuries. There were several different reasons why they did not want to conquer foreign lands including:
1) Violation of individual rights/freedoms- Some anti-imperialists felt that forcing a system of government onto a group of people in a foreign land was unfair. These people felt that a government should be developed based on the consent of the citizens, not by force from an outside country.
2) Abandon American values- Americans value self government and control over their political officials. This is evident from the structure of American society, as citizens get to vote for officials who make laws for us. Forcing control over another country would go against this core American value.
3) In favor of isolationism- This individuals often favored American isolationism and avoiding foreign affairs altogether. They thought that getting involved in foreign wars would distract the US government from the needs and wants of American citizens.