The British taxed goods such as tea in order to pay for government in the colonies. Why would Americans protest the tea tax?

The Americans were angry at the British to start with. They were fed up with being oppressed by them. So, yes, they were angry at the tax on the tea, but they were even more angry with the British government as a whole. The tax was like the straw that broke the camel's back.

Additionally, they would protest this tea tax, because it was funding for more British control in the colonies. The Americans didn't want to pay to be controlled. The Americans wanted freedom and by paying taxes, they were instead supporting British rule.