In Common Sense Paine's principal arguments for independence stem from two basic ideas, in my view. The first involves the English constitution and the system of government of Great Britain. The second is that the American colonies simply no longer need to be connected with Britain. We can examine these ideas, and you can then extrapolate five (or more) specific conclusions Paine reaches as to why the independence of the colonies is necessary.
Paine debunks the claim that the different components of the British government act as checks upon one another. The fact that the monarchical part (the King) still exists is evidence to Paine that the constitution of England is "sickly." In his Rights of Man, written fifteen years after Common Sense, Paine even goes so far as to deny that England, or Great Britain as a whole, has a constitutional system at all. In Paine's view hereditary succession has no place in government, and monarchs are worthless:
Of more worth is one honest man to society and in the sight of God, than all the crowned ruffians that ever lived.
But even if the English system were ideal, Paine refutes the notion that America needs Britain or that there should be any connection at all with the "mother country." This is partly because, according to Paine, Britain's protection of America is due only to self-interest, and because Britain, in the French and Indian War—and at any time—
did not protect us from our enemies on our account, but from her enemies on her own account.
Furthermore, Paine considers the concept of England as the "parent country" of America to be false:
Europe, and not England, is the parent country of America. This new world hath been the asylum of the persecuted lovers of civil and religious liberty from every part of Europe.
This argument is especially interesting because it indicates that America, in 1776, was already a "melting pot," a haven for people from any country, not just England or Britain.
It is also true, says Paine, that since the beginning of hostilities between Britain and America—which, as he wrote Common Sense in February of 1776, had already been taking place for ten months, since April, 1775—all the previous arguments for remaining connected with Britain have been invalidated. "Every quiet method for peace," writes Paine, "hath been ineffectual." Paine enumerates the reasons that, in his view, even if "matters were now made up [i.e., hostilities were brought to an end]," the result would be "the ruin of the continent."
Apart from these specific points asserting that reconciliation is impossible and that America should not be governed by Britain in any event, toward the close of Common Sense Paine elaborates his first point about the British system of government being defective:
The republics of Europe are all (and we may say always) in peace. Holland and Switzerland are without wars, foreign or domestic: Monarchical governments, it is true, are never long at rest; the crown itself is a temptation to enterprising ruffians at home; and that degree of pride and insolence ever attendant on regal authority, swells into a rupture with foreign powers, in instances, where a republican government, by being formed on more natural principles, would negotiate the mistake.
In other words, America should be an independent republic, for its own benefit. To read Common Sense today is to see how influential and prescient Paine was, nearly half a year before the Declaration of Independence was written.