In Thomas Paine's Common Sense: Why are Paine's reasons and rhetoric significant?

Thomas Paine wanted the message of "Common Sense" to be very accessible to his audience, the people of the American colonies. He was contracted to convince as many people as possible that separation from Britain was the right decision at that time.
Paine relied heavily on appeals to logic.  In the quotation below, he anticipated an opposing argument and refuted it.

"I have heard it asserted by some, that as America hath flourished under her former connection with Great Britain, that the same connection is necessary towards her future happiness, and will always have the same effect. Nothing can be more fallacious than this kind of argument. We may as well assert, that because a child has thrived upon milk, that it is never to have meat; or that the first twenty years of our lives is to become a precedent for the next twenty."

Paine's point is that the past practices of Britain may have enabled the colonies to "flourish," but he argues that there is no indication that a continued relationship will continue to yield the same result.  His use of a simple analogy about child rearing would be readily understandable by the masses.
Paine also refutes the claim that Britain should continue to rule the colonies because the people of the colonies are of English descent.  His claim,

"Not one third of the inhabitants, even of this province, are of English descent"

would ring true to people of the colonies in 1776 because there had been an influx of immigrants from all over Europe: Holland, France, Germany, etc. 
Paine doesn't miss  opportunities to appeal to emotion. For example, to those who would say that "Britain is the parent country," Paine counters, "Then the more shame upon her conduct. Even brutes do not devour their young."  
By keeping his message consistent, appealing to both logic and emotion, and using examples and analogies that would be resonant with his audience, Paine built his reputation as the pamphleteer of the American Revolution.
 
 
 
http://www.njhistoryroundtables.org/documents/CommonSense.pdf