Why do they say The Philippines is the 3rd largest English speaking country in the world?

Your figures are wrong and it depends on what you are measuring. If you are measuring by total numbers, they come in 5th. If you measure by percentage of the population, they come in 50th. Incidentally, the U.S. comes in 1st by total numbers, but 12th by percentage. BTW, most native English speakers do not speak proper English and most filipinos speak more than one language. Tagalog is only one of about 170 language spoken in the Philippines.