The British angered the colonists by doing many things. The main reason that the colonists were upset was because of increased taxes. When Britain went to war with the French in the French and Indian war, the country lost a large sum of money and could not afford to pay it back. Therefore, they forced the colonies to pay it back through greater taxes.
Another thing that the British did was move their armies into colonists' homes without the ccolonists' consent.
The Patriots, or Liberty's Boys, would then go on to begin what would be known as the American Revolution. The average townspeople were encouraged to rebel against the British and Loyalists through many acts including what became known as the Boston Tea Party.
Unlike the average citizen of the American colonies, I believe that a more logical step to gain independence would be to simply ask. You see, this is how Canada gained independence. It would also have helped if we imply or even told outright that we would still be allies and trade partners of Britain. I really think that it was the trade thing that got to the king.