Why did the colonists believe Britain could not tax them?

Answer 1

They did not believe that Britain could not tax them. They were just upset that someone from the colonies wasn't there to decide the taxes, hence "taxation without representation". They felt as if their basic rights were violated.

Answer 2

No reasonable person would expect to have a functional government and pay no taxes at all. Benjamin Franklin is quoted as saying that nothing is certain but death and taxes... in other words, it is certain that we will die, and it is certain that we are going to be paying taxes to somebody.

During the reign of George III, taxes greatly increased, which was a source of resentment. Some of the Colonials had traveled to England to present the argument they they should be able to elect a member of the House of Commons ("no taxation without representation").

On top of this, the British East India Company was given a government-backed monopoly so the sole source of tea was overpriced, and the customers, not the company, had to pay the taxes on it.