The bedrock of western ideals that the US was born from contains a lot of influences from Christianity, especially the part where the duty of a good Christian is to spread the faith and convert heathens around the world to the one true faith in order to save them from eternal damnation in hell. Although religiosity as a whole is going down in the western world, this savior complex still persists and echos of it can be seen in how many people in the West feel a need to, as you put it, do something to spread democracy and human rights on the other side of the world regardless of local history or customs because it's for their own good.