There were three major arguments that the colonists used when objecting to the new taxes imposed by the British in these years.
First, they argued that they should not be taxed by a legislature in which they were not represented . This is the famous "no taxation without representation" argument."
Second, they argued that Parliament should only tax for the purpose of regulating trade. They argued that taxes that were meant solely for the purpose of raising revenue went against the (unwritten) British constitution.
Third, they argued that Parliament only had the right to impose taxes on goods that entered and left the colonies. They argued that Parliament had no right to impose taxes on things that were not being traded into or out of the colonies.
All of these arguments were used at various times to oppose the new taxes imposed by the British.