What were some reasons against imperialism?

This answer will focus on American anti-imperialism, though anti-imperialists in other countries held many of the same convictions. People were opposed to imperialism for a very broad array of reasons, some of which may seem contradictory to modern students. Let us look at a few. 

Many argued that imperialism was contrary to American democracy. For most, this was because the United States had its origins in gaining independence from an empire, and having been a...

This answer will focus on American anti-imperialism, though anti-imperialists in other countries held many of the same convictions. People were opposed to imperialism for a very broad array of reasons, some of which may seem contradictory to modern students. Let us look at a few. 

Many argued that imperialism was contrary to American democracy. For most, this was because the United States had its origins in gaining independence from an empire, and having been a colony, it had no business trying to take colonies of its own. In its platform of 1899, the United States Anti-Imperialist League said that "the subjugation of any people is 'criminal aggression' and open disloyalty to the distinctive principles of our Government." 

Another claim often made by anti-imperialists was that imperialism would involve the United States in foreign wars, wars which the nation had been able to keep out of (more or less) for the last century. They watched with unease as European nations built up large navies and armies even as they gobbled up territories around the world, especially in Africa. The connection between imperialism and militarism was strong in the minds of many Americans.

Still others decried the brutality exercised by imperial powers over those they claimed to be helping. Reports of atrocities in the Philippines were read by many Americans, and rather than holding individual American soldiers accountable for them, they tended to view these crimes as endemic to imperialism itself. "We regret," said the Anti-Imperialist League, "that the blood of the Filipinos is on American hands." Mark Twain bitterly satirized the brutality of King Leopold's rule over the Belgian Congo in an imaginary soliloquy that underscored this belief especially well.

Finally, many Americans argued that empire would lead to the absorption of more non-White peoples into the United States. The period of American imperialism also witnessed the advent of Jim Crow in the South--it was a time of extraordinary racism. As South Carolina Senator Ben Tillman, a virulent racist put it, "why do we as a people want to incorporate into our citizenship ten millions more of different or of differing races?" 

So anti-imperialists could oppose the acquisition of colonies for many different and sometimes contradictory reasons.