The American Revolution
When the American colonies declared their independence from Great Britain in 1776, they did so with the belief that it was possible to work out their differences. This belief was based on the idea that the two sides were not so different that they could not find a way to coexist. After all, they were both English-speaking peoples with similar cultures and values.
The reality, however, was that the differences between the two sides were too great to be overcome. The American colonies were fighting for their freedom, while Great Britain was fighting to keep its colonies. The conflict quickly escalated into a full-blown war, and by the end of it, the American colonies were victorious.
Since then, the relationship between the United States and Great Britain has been largely cordial. There have been a few bumps in the road, such as the War of 1812, but overall, the two countries have been able to work out their differences.