In this answer, I will look at the pros and cons of taking the Philippines from the point of view of a person in the late 1800s or early 1900s. I will be looking at what people would have thought about taking the Philippines when that was actually taking place.
There were three main advantages that people thought we would gain from taking the Philippines. First, we would gain prestige in the world. All major European countries at that time had overseas empires. By taking the Philippines, the US would have its first large possession far from its own territory. This would help make us look like an important world power. Second, we would gain military power. By taking the Philippines, we would gain a place where we could have naval bases. Ships based in the Philippines could easily project American power in Asia. Finally, there would be economic benefits to taking the Philippines. We would gain privileged access to Filipino markets, meaning we would be more able to get their resources for good prices and sell them our products as well.
People at that time would have seen two major bad points to taking the Philippines. First, at least some Americans thought that taking the Philippines was immoral. The Filipinos, led by Emilio Aguinaldo, had been trying to gain independence from Spain. It seemed wrong (and un-American) to take away the Filipinos’ chance to be free. People felt that it was wrong for us, a country founded on the principle of freedom from colonial rule, to impose our own colonial rule on others. The other argument against taking the Philippines was that it would be bad for us in racial terms. Many Americans at this time were openly racist. They believed that Filipinos were racially inferior and they did not want to make a large number of non-white people part of America. They feared that taking the Philippines as a colony would eventually force us to allow the Filipinos to be part of our polity and society.