Why did the protestant separatists, or "saints," decide to move to the new world?

They decide to move to the New World for they found the Church of England to be corrupt and idolatrous as the Catholic Church.

Explanation:

In 1608, a group of protestant separatists left their country of England to move to the New World of America in hopes of building a new community devoid of the corrupt and idolatrous community in England. They refused to be associated to the Church of England and also to the Catholic Church.

'The Separatists', as they were known, were critical of the Church of England and their ways. So they separated from it, detaching themselves from the Church and came to America, the "New World" in hopes of starting a new life across the Atlantic. Sailing from Plymouth, these group of "Saints" were transported in a merchant ship "The Mayflower", they reached a deserted Indian settlement which they renamed "Plymouth" from their starting point. These people moved to the New World in hopes of restarting a new life and also to begin a new and better religious as well as societal community away from the English Church and Catholic Church rules.