While more can always be written, versions of this question come up in this sub from time to time, and I have addressed it a couple of times. Most recently, I added an addendum here to my previous answer here.

The TL;DR version is that the Americans weren't ever looking for representation in Parliament - that kind of undercut their argument. Their argument was that they already had representation, in their colonial legislatures, and that was the proper venue for levying taxes. Several of the colonial charters even explicitly empowered the colonial legislatures with taxation authority. This included Massachusetts, where the whole "taxation without representation" issue erupted.

Parliament's argument was that they were superior and could rescind colonial charters at will, so anything they did superseded what the colonial legislatures did. This led to an argument about sovereignty, and the situation between Massachusetts and Parliament deteriorated from there.

However, it wasn't the taxation issue that led directly to war. It was the Intolerable Acts, which took some drastic steps to try to force Massachusetts to comply with Parliament's wishes. But this scheme backfired, and it got twelve other colonies to join in Massachusetts' rebellion.

More information and sources in those previous answers.