Why did separatists come to north America?

The Pilgrims and Puritans came to America in family groups (rather than as isolated individuals) and were mainly motivated by a search for freedom to practice their religion.

Explanation:

The Puritans created a deeply religious, socially tight and politically innovative culture that is still present within the modern United States. They expected this new land to serve as a "redeeming nation." They fled England and, in America, tried to create a "nation of saints": an intensely religious and completely just community designed to be an example for all of Europe.

They came for religious freedom. And they also wanted to completely separate from the Church.