Question: Why did the American Whigs believe Parliament couldn't tax the colonies?
About the article "Boston Tea Party", section "Townshend duty crisis".

Candidate passages:
Controversy between Great Britain and the colonies arose in the 1760s when Parliament sought, for the first time, to impose a direct tax on the colonies for the purpose of raising revenue.
Some colonists, known in the colonies as Whigs, objected to the new tax program, arguing that it was a violation of the British Constitution.
Britons and British Americans agreed that, according to the constitution, British subjects could not be taxed without the consent of their elected representatives.
In Great Britain, this meant that taxes could only be levied by Parliament.
Colonists, however, did not elect members of Parliament, and so American Whigs argued that the colonies could not be taxed by that body.
According to Whigs, colonists could only be taxed by their own colonial assemblies.
Colonial protests resulted in the repeal of the Stamp Act in 1765, but in the 1766 Declaratory Act, Parliament continued to insist that it had the right to legislate for the colonies "in all cases whatsoever".
When new taxes were levied in the Townshend Revenue Act of 1767, Whig colonists again responded with protests and boycotts.
Merchants organized a non-importation agreement, and many colonists pledged to abstain from drinking British tea, with activists in New England promoting alternatives, such as domestic Labrador tea.
Smuggling continued apace, especially in New York and Philadelphia, where tea smuggling had always been more extensive than in Boston.
Dutied British tea continued to be imported into Boston, however, especially by Richard Clarke and the sons of Massachusetts Governor Thomas Hutchinson, until pressure from Massachusetts Whigs compelled them to abide by the non-importation agreement.
Parliament finally responded to the protests by repealing the Townshend taxes in 1770, except for the tea duty, which Prime Minister Lord North kept to assert "the right of taxing the Americans".
This partial repeal of the taxes was enough to bring an end to the non-importation movement by October 1770.
From 1771 to 1773, British tea was once again imported into the colonies in significant amounts, with merchants paying the Townshend duty of three pence per pound.
Boston was the largest colonial importer of legal tea; smugglers still dominated the market in New York and Philadelphia.
By the time the Declaration of Independence was adopted in July 1776, the Thirteen Colonies and Great Britain had been at war for more than a year.
Relations between the colonies and the mother country had been deteriorating since the end of the Seven Years' War in 1763.
The war had plunged the British government deep into debt, and so Parliament enacted a series of measures to increase tax revenue from the colonies.
Parliament believed that these acts, such as the Stamp Act of 1765 and the Townshend Acts of 1767, were a legitimate means of having the colonies pay their fair share of the costs to keep the colonies in the British Empire.
Many colonists, however, had developed a different conception of the empire.
Because the colonies were not directly represented in Parliament, colonists argued that Parliament had no right to levy taxes upon them.
This tax dispute was part of a larger divergence between British and American interpretations of the British Constitution and the extent of Parliament's authority in the colonies.
The orthodox British view, dating from the Glorious Revolution of 1688, was that Parliament was the supreme authority throughout the empire, and so by definition anything Parliament did was constitutional.
In the colonies, however, the idea had developed that the British Constitution recognized certain fundamental rights that no government—not even Parliament—could violate.
After the Townshend Acts, some essayists even began to question whether Parliament had any legitimate jurisdiction in the colonies at all.
Anticipating the arrangement of the British Commonwealth, by 1774 American writers such as Samuel Adams, James Wilson, and Thomas Jefferson were arguing that Parliament was the legislature of Great Britain only, and that the colonies, which had their own legislatures, were connected to the rest of the empire only through their allegiance to the Crown. 
The association of Toryism with the Lord North's government was also influential in British North America, and writings of British political commentators known as the Radical Whigs did much to stimulate colonial republican sentiment.
Early activists in the colonies called themselves "Whigs", seeing themselves as in alliance with the political opposition in Britain, until they turned to independence and started emphasising the label Patriots.
Later, the United States Whig Party was founded in 1833, focused on opposition to a strong presidency, just as the British Whigs had opposed a strong monarchy. 
 1766 Grenville, unpopular with the king, was dismissed when the Rockingham Whigs agreed to form a government under Prime Minister Charles Watson-Wentworth, 2nd Marquess of Rockingham.
Rockingham's government successfully repeals the unpopular Stamp Act on condition that the Declaratory Act is passed, which asserted the right of Parliament to pass laws in the American colonies.  
The Currency Acts created tension between the colonies and the mother country, and were a contributing factor in the coming of the American Revolution.
In all of the colonies except Delaware, the Acts were considered to be a "major grievance".
When the First Continental Congress met in 1774, it issued a Declaration of Rights, which outlined colonial objections to certain Acts of Parliament.
Congress called on Parliament to repeal the Currency Act of 1764, one of seven Acts labeled "subversive of American rights".
However, according to historians Jack Greene and Richard Jellison, the currency debate was no longer really a "live issue" in 1774, due to the 1773 amendment of the Act.
The controversy's most important impact was psychological, in that it helped convince many colonists that Parliament did not understand or care about their problems.
Colonial leaders came to believe that they, rather than Parliament, were better suited to legislate for the colonies.