In "The Crisis," Paine directly quotes, or really paraphrases, from the Declaratory Act—passed by Parliament in 1766—when he writes,
Britain, with an army to enforce her tyranny, has declared that she has a right (not only to TAX) but to "BIND us in ALL CASES WHATSOEVER." [The capital letters are Paine's and indicate direct quotes from the Declaratory Act]
He chooses this quote because of its rhetorical value. Note that he emphasizes the word "bind," which has connotations of bondage and slavery, on which he then elaborates in the same sentence of the pamphlet:
[...] if being bound in that manner, is not slavery, then is there not such a thing as slavery upon earth.
In truth, the Declaratory Act was passed by Parliament after that body repealed the Stamp Act in a concession to fierce American protests and anger by British merchants hurt by colonial boycotts. While...
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backtracking on the Stamp Act, Parliament did not want to concede the point of the colonial protests, which was that Parliament had no right to tax the colonies, who were not represented in it. The Declaratory Act was intended to state that Parliament did, in fact, have that power, as well as the power to legislate for the colonies more generally. Paine uses it to show that the colonists never would have had equality within the British Empire. So quoting the passage from the Declaratory Act allows him to score a propaganda point by connecting a word associated with slavery with the colonists.
References
It is not clear to me which particular article of "The Crisis" you are talking about. There's more than one place where he quotes one British person or another. With that in mind...
The best reason for Paine to be using the words of the British in his articles is because they actually help him make his argument. When your opponent says something that helps you, it's better to quote his actual words rather than trying to paraphrase. It makes your argument sound stronger and makes him look dumb because he's saying stuff that helps you.
So when he quotes Howe's words about the Congress, for example, they help him make the point that America does not need Britain or its help.
If you're talking about a particular quote and still need help, let me know...