“No taxation without representation” is also a drastically misunderstood line.

What they were effectively asking for was self-governance, being removed from parliamentary control.

Given the technological limitations of the time, there was no way to effect a representative scheme in parliament with a constituency that was a 12-week round trip away. Furthermore, there were serious discussions of adding seats to parliament for the colonies, and the colonies refused to send anyone.

The Assembly of Massachusetts Bay was the first which ever took exception to the right of Parliament to impose Duties or Taxes on the Colonies, whilst they had no representatives in the House of Commons. This they did in a letter to their Agent in the summer of 1764 … And in this letter they recommend to him a pamphlet, wrote by one of their members, in which there are proposals for admitting representatives from the Colonies to fit in the House of Commons … an American representation is thrown out as an expedient which might obviate the objections to Taxes upon the Colonies, yet … it was renounced … by the Assembly of the Colony which first proposed it, as utterly impracticable.

And

Whilst [the radical colonists] exclaim against Parliament for taxing them when they are not represented, they candidly declare they will not have representatives [in Parliament] lest they should be taxed … The truth … is that they are determined to get rid of the jurisdiction of Parliament … and they therefore refuse to send members to that assembly lest they should preclude themselves of [the] plea [that Parliament’s] legislative acts … are done without their consent; which, it must be confessed, holds equally good against all laws, as against taxes … The colony advocates … tell us, that by refusing to accept our offer of representatives they … mean to avoid giving Parliament a pretence for taxing them