What arguments were made for annexing the Philippines?

Probably the argument which carried the most weight was that if the US did not take over the Philippines, after having ejected the Spanish, then some other European power or Japan surely would. Germany, Italy, France, Japan, Russia and Great Britain were at that time busy greedily grabbing chunks of China as fast as they could get their hands on them. All cast covetous glances in the direction of the Philippines, and had the US not remained its almost a certainly that one or another would have been unable to control its acquisitive impulses.

Another was that the Spanish, in their 300 years of colonialism in the Philippines, had done absolutely nothing about educating the people. There was no real native upper class or intelligentsia, no one the US would have felt safe in entrusting the nation too. The Philippines have about one thousand islands and almost as many distinct cultures and languages. There were natural leaders among the Filipinos but none the US felt would be able to successfully fend off colonizing Europeans, or Japan. This was the argument used to try to sell the idea to the American people. It was a civilizing mission, to educate the Filipinos and fit them for western-style self-government.

The Republicans of the day also thought it was a wonderful thing that they had won an Empire for America. Of course, the US presence in the Philippines was the prime reason the Japanese felt the need to attack the US in December, 1941, so maybe it did not work out as well as the Republicans said it would.