From a historical point of view, there is nothing or very few things that are inevitable. Things only seem inevitable from hindsight; things could have gone another way. For example, if the British won the Revolutionary War, American could still be a part of England and part of the Commonwealth.
That said, a few things slant (that is the key word) that there would be a split.
First, there is the problem of distance. America, from a geographic point of view, is far from Great Britain. This argues for independence, but this fact alone means little.
Second, there is the independent spirit and growing individualism of America. This is one of the things that separated America from other nations - a radical individualism.
Third and more determinative, most of the people in America were Protestants. Therefore, they were outside of the Anglican church. Moreover, the spirit of Protestantism was one of independence. And the Puritans left England, in part, for religious freedom.