The three don't like each other for a number of reasons.

Mindanao doesn't much like the other two because they keep bashing on his choice of religion, which makes him want to break free from them all the time.

Visayas doesn't like the other Luzon because she absolutely insists on making Cebuano the Philippines' national language.

Luzon is jealous of his siblings because tourists like going to them more.

Philippines has to break them up ever argument because she can feel herself hating herself.