History books generally tell us that the French and Indian War was the turning point that, eventually, led to the American Revolution and to the ultimate split between the colonies and the United Kingdom.  There are at least three reasons why this war is seen as a turning point.

First, the war gave colonists more of a feeling that they were similar to one another and different from the British.  Before the war, the colonists had generally seen themselves as citizens of their own colonies, not as Americans.  During the war, however, men who went off to fight generally mixed with men from other colonies and came to realize that they were very similar to one another.  In addition, they came to believe that they were very different from the British soldiers.  They were, for example, more independent and less willing to allow officers to mistreat them.  This reinforced in the colonists the idea that they were all similar to one another and, importantly, that they were different from the British because they loved freedom more.  All this gave them a reason to feel that they were no longer British.

Second, the war got rid of the threat of France.  Before the war, France had a large amount of territory in North America.  The colonists would have known that France might attack them if they were not protected by the UK.  For this reason, they would have been less likely to think independence was a good idea.  They would have been more likely to think that they would be too weak to protect themselves as an independent country.  When the French left North America after the war, it allowed the colonists to think that they might be able to survive if they broke away from Britain.

Finally, and most importantly, the war changed the way the British government treated the colonies.  The war was very expensive and the government wanted the colonies to pay (what it saw) as their fair share.  Therefore, the government started to impose more taxes on the colonies.  It also started to be more aggressive about trying to stop smuggling into and out of the colonies, which was a very lucrative profession for some colonists.  When the government did this, the colonists felt their rights were being violated.  The British government had not acted like this before and they had grown to feel that they had the right to be free from much taxation and the right to trade with whoever they wanted (even if it was technically illegal).  When the government changed its behavior because of the war (notably with the Stamp Act), the colonists became very angry.  This led them to want to rebel against the British.

For all of these reasons, the French and Indian War is seen as the turning point that caused the colonies to want to break away and to cut their ties to the British Empire.