I'm studying American government right now, and this question came to mind. The American colonies seemed very prosperous compared to other places, and they didn't appear to have it that bad either, yet they believed that their "inalienable rights" were being violated by the king. The people in Britain didn't rebel like the colonists did. So what was it about the people, the Founding Fathers in particular, that made them believe differently about government and the rights of individuals? Was it the people who settled there, such as the Puritans or Quakers? Or something completely different?
Remember that, right up until the colonies declared independence, most Patriots were fighting to defend their British liberties. 18th century country Whig political thought held up the rule of law and the restraints on power as the best part of the British system. It was also an intensely paranoid political worldview, as power worked constantly worked through various forms of corruption to erode men's liberties. From this point of view, taxation without representation was a particularly odious government policy, as it subjected Americans to the power of men they had no ability to influence legally. In that sense, their condition seemed not that different from slavery.
Still, that only gets us halfway there. This still doesn't explain why Americans resorted to violence and armed resistance instead of working within the impressively flexible British system.
For that, we need to look at the colonists' pre-Revolution views of Britishness. As people living on the periphery of the British empire, well-to-do colonists tried very hard to announce their claim as equal subjects of the empire. They followed British fashions and trends closely, and spent much of their disposable income on imported British luxury items so that they could ape the island's gentry. In a lot of ways, they were trying to out-British the British. This included what could be seen as an overreaction to the threat to their British constitutional rights by Parliamentary taxation.
See: Bernard Bailyn, The Ideological Origins of the American Revolution
T. H. Breen, The Markelplace of Revolution
Patrick Griffin, America's Revolution
This isn't really my subject area, but since nobody else has responded so far I'll give my thoughts on this.
The people in Britain didn't rebel like the colonists did.
Didn't they? The American Revolutionary War began only 30 years after the battle of Culloden, which finally ended the Jacobite rebellions. These rebellions were the result of another rebellion of sorts, one which was actually successful: the so-called Glorious Revolution, when the Catholic James II was deposed and replaced by the Protestant William of Orange. Several years prior to this there had been another rebellion against James II in the west of England, led by the Duke of Monmouth. And if we go back a few decades further, we come to the bloody period of the British Civil Wars, when Parliament rebelled against King, Army rebelled against Parliament, etc etc - you could characterise the whole period as a succession of rebellions which ultimately came full circle, resulting in the Restoration of the monarchy in 1661. So I think your assumption is inaccurate: rebellions weren't inherently American, and the American Revolution built on a long history of British rebellions and counter-rebellions.