What was the colonists biggest objection to paying taxes to the british government

They did not elect members to Parliament and so believe the Parliament had no right to tax them.

Explanation:

Before the Revolutionary War, there was a lot of tension between the colonists and the British government. The colonists believed that in order for taxes to be considered legitimate, they should enjoy representation in Parliament. This is because the taxes were being used for laws that they should have been able to decide upon. However, the colonists did not elect members to Parliament. This idea was summed up in the phrase "no taxation without representation."