Why is New York not considered to be part of New England?

What we now know as New York was originally a Dutch settlement. It was the Dutch who established the first European colonies in this part of the New World, founding a number of settlements along the Hudson River. One such settlement, the most famous of all Dutch settlements, was New Amsterdam.
The Dutch maintained control of their colonies for the better part of sixty years. But during this time, they were locked in a prolonged and bitter battle for naval supremacy with the English, who coveted Holland's American colonies, hoping to add them to the landholdings they'd already acquired in the New World.
Given England's undisputed mastery of the sea it was only a matter of time before she took over the Dutch settlements. And this is precisely what happened in 1664. What had been the colony of New Netherland became New York, named after James, Duke of York, King Charles II's younger brother and the future King James II. And once the English seized the settlement of New Amsterdam, they also renamed it New York, the name it has retained to this very day.