This is political, so it has elements of arrogance and greed and cultural chauvinism, but there's also a lot of politics. Part of the reason to colonize N. America for the English was to get rid of troublesome groups within the country. England had a lot of religious groups that were a pain in the ass to governing powers. They could warehouse them in North America where they were kind of out of sight, out of mind.

Spain had all these people that were no longer needed to fight the Moors. Having a large warrior class with nothing to do is dangerous. Letting them conquer another territory was unifying and focused trouble away from home.

France had severe budgetary problems. Colonies might provide the king with financial relief, and leverage against his own nobles, if enough wealth could be extracted.

The 30 Years War/War of Spanish Succession had put the Netherlands in a precarious position. Without population, they'd have to rely on mercenaries. Colonies provided a potential source of revenue to pay those mercenaries without levying heavy taxes on the local populations.

Countries were jealous of the wealth their competitors were achieving and wanted to gain stature against their neighbors.

This stuff is all very multifaceted and some reasons can be stated more openly than other reasons. Saying you want to Christianize the New World is great PR for Spain. Saying you need to find something to do with all these blood thirsty ruffians from Extremadura so you're going to send them to the edge of the world on some harebrained scheme is not. So you say one real loud and whisper the other.

The racism is a little more complicated. There's good research and writing on how it developed out of the needs of imperialism and probably wasn't a cause of imperialism, but it's awful offspring, until maybe beginning in the 17th century.