This comes from the reason for the revolt. After the English Civil War the colonies had been basically operating by themselves with little interference from London.

However after the seven years war and the glorious revolution the new British state was heavily in debt and so needed to raise taxes. For London it looked like the colonies hadn't been contributing much to the empire.

As such they began to increase their control over the territory and increase taxation. The American colonists didn't like this as they'd gone through decades of running their own affairs. Now they tried to come to an agreement on this by demanding a member in parliament seeing that if they must pay taxes then they should have a say in both its design and use.

When London refused the local elites decided it was better to go it alone. The argument going that they were only trying to preserve the status quo.

Hope that helps.

There are a couple of other strands to this argument in addition to the one the one well summarized by Exostrike. The principal grievances expressed in the first Continental Congress arose out of the Seven Years' War, concluded in 1763. Questions of revenue and taxation were certainly important, but there was also deep resentment over the British decision to allow self-government to the French-speaking colonists in Quebec and the Northwest Territory, which the American colonists thought should have been given to them, to colonize (eventually they succeeded in colonizing the Northwest Territory, after the successful Revolution). The third strand has to do with slavery. There was a rising Abolitionist movement in Great Britain, especially hostile to the slave trade, which UK eventually banned. In 1772, in Somerset's Case, Lord Mansfield held that slavery was inconsistent with the common law, a result that would have allowed northern colonies to free escaped slaves. The enthusiasm for independence and eventually for a federal constitution owes something to the concerns that Britain would upset the status quo in the colonies with regard to slavery. See Alfred W. Blumrosen & Ruth G. Blumrosen, Slave Nation (2005); Charles W. Mills, several articles and books, especially The Racial Contract.

It's not true.

In terms of modern day "conservatism." Yes, the colonists opposed higher taxes much in the same way that modern day Republicans do.

That however, does not make the British Empire "revolutionary."