The American colonists were driven to declare war on the British Empire, because they were being oppressed, and not treated as citizens. They believed that the British had no right to impose more taxes on them, and so declared independence
The declared war because the British were giving taxes on the colonists without giving them the right to vote in parliament which was a right they used to have in England. Many other events lead the colonists to delclare war, like: -The French and Indian War -The Quartering Act -The Stamp Act -The Townsend Act -The Boston Teaparty -The Boston Massacre (to name a few)
The Jay's Treaty, Monroe Doctrine, and Adams-Onis Treaty forced the British to leave the Eastern US (and pretty much all of the America's) and they 'forced' Spain out of Florida.