The colonists believed they should not be taxed by Parliament because they did not have direct representation in Parliament. The colonists argued that since they did not have members of Parliament representing their interests, Parliament did not have the authority to tax them.
The colonists felt that they should only be taxed by their own colonial assemblies, where they were directly represented. They believed that this was a fundamental right of Englishmen, which was enshrined in the Magna Carta and other English legal traditions. The colonists saw themselves as loyal British subjects, but they also believed that their rights as Englishmen were being violated by the actions of Parliament.
This belief was a major factor in the lead-up to the American Revolution, as the colonists began to resist British taxation and other policies that they saw as infringing on their rights. The slogan "no taxation without representation" became a rallying cry for the colonists and a symbol of their resistance to British rule.