Why did President McKinley and the Republicans jump at the chance to hold the Philippine Islands?

They saw them as key to American influence in the Asian Market

Explanation:

The Philippines islands is located in a very close proximity between China, India, and Indonesia. Those countries has the 1st largest population, 2nd largest population, and 4th largest population respectively.  With the combined market share of 2.8 Billion potential customers.

Controlling the trade route in this strategic location will give united states a massive leverage in Trading with the Asian Market.  In order to hold this country close to American influence, President McKinley and the Republicans placed a military base in Philippines in early 1900s.

I know I'm very late but ill leave it up here for anyone else that needed the answer like I did.

"Maintain the strong arm of authority to repress disturbance and to overcome all obstacles to the bestowal of the blessings of good and stable government upon the people of the Philippines Islands under the free flag of the United States."

well this isn't a question but if you are asking if it is true or false it is, true.