British historian here- this is to compliment what the excellent American chap said above.

Some additional factors: The economic causes off the American Revolution are much overlooked. In 1772 there had been a massive credit crisis in London (almost identical to the 2008 one) which had caused huge economic disruption. The British just about survived but it changed the entire financial market. The Colonies were very badly hit.

Part of the reconstruction of the economy had been the British bailing out the Honourable East India Company, considered ‘too big to fail’. The government wanted at least some of the cash back. The EiC had a plan to do so. Sell lots of tea direct to the US colonists.

The problem was? EiC tea was heavily taxed if they sold it direct. The colonies were a huge market for tea but because of the high prices of tea in London they usually sourced their mainstay of the product from the Netherlands (where the Dutch version of the East India Company sold cheaper tea). Thus across the Atlantic a successful network of tea smugglers emerged.

In order to compete with this? The Tea Act CUT the tax on tea from the EIC. Making it affordable. That’s won’t most folks don’t realise. It was about a tax cut.

Local smugglers in Boston realising that cheap legal tea would destroy their businesses basically did the Boston tea party in order to prevent this- but while it was a tax cut that started the issue, the principle of anykind of taxation without direct democracy became a huge cause and we end up with the revolution.

I mention all of this for good reason. The EiC after the peace of Paris basically ended up becoming a state within a state. It was the East Indian Company as a corporation that began the subjugation of Indian states.

The American War of Independence had seen the French, the Spanish, the Dutch and the Indian state of Mysore all kinda support the American colonists by declaring war in Britain; in the aftermath Britain turned a blind eye to the EiC in India, whose basically a mercenary commander, Robert Clive, subjugated, conquered and took large chunks of India.

The EiC in time became as formidable army/navy. It remains the worst example of unlimited corporate power really. The British eventually took over running India because of their excesses and thus we have the Raj.

There is a lot more too it, but if you get into it you will see how seriously interconnected everyone was.

American here. Part of the reason the colonies revolted was that they felt like an accessory to the British, if that makes sense. One of the great rallying cries of the time was "no taxation without representation!" crying out against a lack of representation in the Parliament that decided how much to tax them. Taxes from a foreign power across the sea that didn't represent you felt, to the Americans at least, like something of a bad deal.

Why were the British raising taxes? For all intents and purposes, Britain was fresh off a war it fought for the colonies. The French and Indian war (Indian as in Native Americans, not as in the country of India) was a battle over Ohio, basically. The colonists were the ones to benefit from this war, or at least that's what Britain said, so taxes were raised on the Americans. The Stamp Act (a tax on printed paper goods), the Townshend Acts (taxes on glass, lead, paint, and a few others), and most famously the tax on Tea (done in part to keep a struggling East India Company afloat).

Growing tensions by American patriots led to acts of the violence, like the Boston Massacre. The Boston Tea Party involved throwing lots of that tea into the harbor. A Continental Congress was gathered, and made a list of grievances (not asking for independence, yet) denouncing taxation without representation and the keeping British armies in the colonies without consent. In April of 1775 British soldiers marched to Concord to seize weapons there, and local militias were assembled. The Revolutionary War began with shots fired at Lexington and Concord.

You mentioned how the British were fighting their own dudes, and in a way, that's what the British felt it was like once the fighting began. It was, at least for the British, a civil war, and was considered something of a minor concern. Part of the reason for American successes was just that Britain wasn't sending its best, instead sending second sons to win a bit of fame or get experience. Americans weren't all universally Patriots either, with a fair number of loyalists supporting the Crown. With support from foreign powers across the sea, America would eventually fight to gain its independence. For example, the Marquis de Lafayette, a French noble, and in fact the area I live in is named after him. I suppose that brings us to the differences.

Most notably, you chaps didn't have to fight a war to become independent. If I'm correct, Britain just realized it couldn't hold on the Raj anymore and just let go. That is quite different from America, where conflict lasted for years. However, there are of course similarities. A general feeling of being governed by people who are fundamentally different, and not having representation. You might be able to find similarities between the Princely States and the idea of American states. At least at first, the colonies weren't strongly united (they were 13, not 1), and early federal government was notoriously weak. The Sepoy revolt is similar, with revolts against a foreign power, but there are of course differences, like all things. Notably, India already had some idea of government set up. You had Princely States and previous rulers before the British came, but in America you had little government (nothing against the natives, but something tells me the colonies were not going to adopt native government) before Britain. Both countries would have done administrative changes after independence, of course, but that difference of independence war vs. somewhat mutual split shows here as well. America was just sort of... plopped into the world, while Britain took steps to help India come out onto the world stage, and with things like the Two Nation theory. Not to say British rule was good, but Britain did take steps to make letting India go a little less painful than open war.

Do feel free to ask if anything was confusing or worded weirdly.