Why were the colonists angry about taxes?

The colonists were angry about taxes because Great Britain for many years had practiced a policy called "salutary neglect" in which they did not collect the taxes and tariffs that they were legally entitled to. Everyone with power, British and American, was making money hand over fist, so if the colonists were illegally trading on the side with countries other than Britain or letting non-British goods into ports without paying tariffs, the British didn't much care or want to pay to send officials to enforce the law.
The French and Indian War, however, was quite costly to the British, and since they had fought it, from their point of view, for the benefit of the colonists, they felt the colonists should help pay for it. The British began to enforce their existing tariff laws and imposed some new taxes (which some historians have argued were actually quite reasonable, given the wealth in the colonies). However, the Americans had been so used to running their own show and doing almost everything their own way that they became angry at what looked like British intrusion into their affairs.
Many historians have come to believe that the British made a mistake with salutary neglect, because it meant that the Americans got very used to running their own show independently. When the British tried to reassert their authority, it felt like tyranny.