Why did Philip of Spain want to overthrow Elizabeth from the throne?

Because she was Protestant. As a result, she threatened Catholic hegemony on the Continent. The 16th Century featured a number of wars between Catholic nations and Protestant upstarts. There are a number of reasons people and nations will fight. They will fight for power, for control of an area. They will fight for territory, to expand their borders. They will fight for resources, whether its food or oil. And, they will fight for religion. And if the Pope (or, today, an imam) says that you will go to heaven if you die for the faith, that provides strong incentive to fight.