Final answer:
The American colonists believed "no taxation without representation" violated their rights as British subjects because they had not consented to direct taxation and were not allowed to elect representatives to the British Parliament. The colonists saw taxation by unchosen representatives as a denial of their rights, while the Parliament believed in "virtual" representation. The colonists also believed it was acceptable for Parliament to regulate trade through taxes, but not to raise revenues without their direct representation.
Step-by-step explanation:
The American colonists believed that "no taxation without representation" was a violation of their rights as British subjects because they had not consented to direct taxation, which they viewed as a reduction of their status as free men. They based this idea on the principle that the people or their representatives should have the right to consent to taxation, as stated in documents like the Magna Carta and the English Bill of Rights. The colonists were not allowed to elect representatives to the British Parliament, so they felt that taxation by representatives they had not voted for was a denial of their rights.
The British Parliament had a hard time understanding this concept because all British subjects were required to obey the laws passed by Parliament, including paying taxes. The Parliament believed in the idea of "virtual" representation, where representatives elected by those who could vote made laws on behalf of those who could not. However, many colonists argued that anything except direct representation was a violation of their rights as English subjects.
In addition, the colonists believed that it was acceptable for Parliament to impose taxes to regulate trade because they saw it as a way to protect the British Empire's interests. However, they did not think it was right for Parliament to raise revenues through taxation without their direct representation, as they felt it violated their rights.