Yeah, "taxation without representation" was short, easily understood, and infuriating, so it was the best way for the Patriots to get people convinced and involved. Getting into trade inequities and political theory and a lot of terms ending in "-ism" isn't really relatable to the common man.
Ultimately, the biggest reason was because the Colonists started seeing themselves as Americans (or Virginians, or New Yorkers, or whatever) rather than the British. That led, quite predictably, to resentment over King George and the British treating the Colonists as second-class citizens, which they did, interfering with our God-given right to smuggle by giving breaks to the East India Company, which they also did, and by responding to our righteous tea protestin' with the super-restrictive and unfair Intolerable Acts. So a lot of it was that we didn't like being clamped down on but, yeah, taxing the hell out of us in several waves, ostensibly to make money to pay for the French and Indian War, didn't go over very well, either.
So the British closed the Port of Boston in 1774, all 13 Colonies got pissed on Massachusetts' behalf, we threw down in '75, adopted the DoI in '76, and here we are.