After reading Chapter 12 of A People's History of the United States, why do you think it took the US military three years to defeats the "insurrectos?"
Zinn is not mainly concerned with why the US took so long to defeat the Filipinos. He is mainly interested in arguing that the war was brutal and racist and that many Americans opposed it. The main thing that he says to explain the difficulty is that the "insurrectos" had the support of the Filipino people.
This is, of course, a major reason that it took so long. However, it is not the only reason. (It is also not completely true as there were many Filipinos who were not opposed to becoming a US territory.) Another major reason is that the Philippines is a large country with almost as much land mass as California. Much of the land is mountainous and covered with jungle. Because of this, there were many places for the rebels to hide. This allowed them to continue to resist for a long time.