The laying a Country desolate with Fire and Sword, declaring War against the natural rights of all Mankind, and extirpating the Defenders thereof from the Face of the Earth, is the Concern of ever Man to whom Nature hath given the Power of feeling. (I.4)
Thomas Paine is certain that, in one way or another, Britain has already declared war on America. Now it's just a matter of fighting back. To make anyone queasy about the idea of war feel better, Paine states that a war from American independence will affect freedom all over the world.
The most plausible plea, which hath ever been offered in favour of hereditary succession, is, that it prevents a nation from civil wars. (2.18)
Paine knows that some people think a hereditary royal ruler is a good idea because it keeps a country stable and stops it from falling into constant civil war. In the end, though, he thinks this argument is garbage. England has always had a king and it's gone through more than a dozen civil wars.
In England a king hath little more to do than to make war and give away places; which in plain terms, is to impoverish the nation and set it together by the ears. (2.24)
Paine rejects the arguments in favor of having a king because the only powers a king has are destructive ones, like declaring war and sending his country into debt. Notice that both of these things involve consequences that the king doesn't have to deal with afterwards.
Arms, as the last resource, decide this context; the appeal was the choice of the king, and the continent hath accepted the challenge. (3.2)
For Paine, the King of England has had every opportunity to treat the American colonies with respect and love. But he has thrown away these opportunities to be a tyrant, so now there needs to be a war for American independence.
Because, any submission to, or dependence on Great Britain, tends directly to involve this continent in European wars and quarrels. (3.18)
Many Americans don't want to fight Britain because they don't like war. But as Thomas Paine points out, being a British colony actually drags America into even more wars because it gets caught up in all the drama Britain has with other countries.
Europe is too thickly planted with kingdoms to be long at peace, and whenever a war breaks out between England and any foreign power, the trade of America goes to ruin, because of her connection to England. (3.19)
Again, Paine insists that remaining under British rule will actually result in more war for America than simply fighting to be free. Britain has all kinds of beefs with all kinds of countries, and when it comes time for war who do you think Britain sends to fight on its behalf? You got it: people from its colonies.
But the most powerful of all arguments, is, that nothing but independence, i.e. a continental form of government, can keep the peace of the continent and preserve it inviolate from civil wars. (3.38)
Thomas Paine is certain that the only way to prevent civil war in America is to give the country its independence. He's certain of this because America has the chance to become a true democracy run by elected officials instead of kings, which can keep the citizens happy and thus prevent civil war.
The republics of Europe are all (and we may say always) in peace. Holland and Switzerland are without wars, foreign or domestic. (3.41)
As Paine points out, countries with democratically elected leaders tend not to have civil wars the way that countries with kings do. That's obviously because the people living in king-ruled countries get frustrated with having a tyrant who they never elected in the first place… and also because kings are bullies who constantly start fights with other countries.
No country on the globe is so happily situated, or so internally capable of raising a fleet as America. (4.10)
Many Americans wouldn't want to go to war with Britain because they'd be afraid America didn't have the power to raise a proper army or navy. Paine wants to put this doubt to rest by showing all his readers exactly why America has this ability: coastline and resources, baby.
[Our] military ability, at this time, arises from the experience gained in the last war, and which in forty or fifty years time, would have been totally extinct. (A.10)
At this moment in history (1776), America has a lot of citizens who are still experienced from the last war that affected America. If they wait too long, though, these veterans will get too old to use their knowledge to help America defeat Britain.