Why do we spell the country as ‘Philippines’ but the language as ‘Filipino’?
Philippines is an old English name of the country. It was a Spanish colony, the Spanish name for the country is Islas Filipinas. Then the people of the Philippines decided to choose a new language to become the national language. They chose a language called Tagalog. Tagalog called the Philippines the same way as Spahish.
Subsequently they decided to rename Tagalog to Filipino to highlight its role as a national language. And English just borrowed the name.