Though that being said, one does also wonder why the British didn't simply grant their colonies voting rights in Parliament. The Americans would've had, what, 1 or 2 MPs with no real power to affect anything and extremely long communication times with their constituencies, but at least they'd have been represented.
Edit: Never mind that last part, seems the numbers in my head were badly off, see the next reply.
Sigh.
This is a good question for a student to have, and the answer is to the history is that it is complicated, but not really complicated just full of details that exhaust the mind.
1st) Remember in the 1770s they had a very different system of how parliament was assembled for all the parliamentary reform things that occurred in 1800s (aka stuff like Rotten Boroughs that was half fixed with the reform act of 1832 but also other reform acts also changed the details, blah, blah, blah.) Aka the arguments that there was "virtual representation" in Parliament already without even giving the colonies representatives for everyone was a UK citizen. I am going to skip into the nuances of the debate between dozens of people including Edmund Burke and others for I just do not care. But yeah before the revolutionary war there was a 10+ year debate in Parliament and people outside parliament and before the war officially started with the Declaration of Independence (but after hostilities / the powder keg had started even though it was not lit yet.) Parliament itself agreed that no taxes without representation but the colonies had to do law and order with the "Conciliatory Resolution."
What I am saying with #1 history is complicated, and this issue is complicated and we are no longer taught history instead we are taught the myth.
2nd) Remember to some people in America it was an all or nothing thing, they did not want some members in parliament for the amount of power they have would be small (aka a faction) and they feared this small faction will not have enough power to protect their financial and other interests. In other words they used the rallying cry of No Taxation without Representation but at the same time they did not want representatives, but instead they wanted self rule for only self rule would protect certain interests they had involving international trade and blah blah blah. Put another way it was never in good faith.
To the people who hold this view in #2 the only form of government was seen as legitimate was a government where their interests that they valued were made possible, to these people the Empire was just to big and they did not agree people 3000 miles away should control their destiny. It is not about self-representation it was about liberty and self-determination for these people.
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I apologize if sound like a condescending ass in this post, and I am not providing all these historical references that will reinforce and argue my point. I do not have the energy to have "a debate." The history is done, it is now in the past, it can't be changed.
So yeah Legolas you are asking a good question, and I want you to know this. The question is very good! Yet the answer though is complicated and the matter is now settled. The answer can not satisfy / gratify.
It is like asking why did World War I have to happen. ¯_(ツ)_/¯ it happened, and if we changed a few details it didn't have to happen, but time machines don't exist, Time's arrow neither stands still nor reverses. It merely marches forward.
Thus the sigh, the title of this post. 
