Why did the Puritans compare themselves to the ancient Israelites?

One sentence response

Because they also believed they were people chosen by God, that were oppressed and exiled.

Explanation:

Puritans believed that they had to escape Europe because of the oppression of the English government. They regarded America as Promised land that was given to them as God's chosen people.

This is of course in contrast to reference in the Bible, when Jews fled Egypt, and went into promise land of Canaan.