Why do you think that the Anti-imperialist League Platform authors refer to the "might makes right" idea as an " ancient heresy?

The correct answer is to emphasize that the democratic traditions of the US do not support imperialism

Imperialism was against everything that the United States stood for since their inception. That's why the concept of might makes right is an ancient heresy because it contradicts the first laws ever set in the United States and that is those of democracy, since imperialism has no democracy in it.