There are two major arguments against gun control, one based on rights and one on safety.
We can argue against gun control on the basis of the Second Amendment. The Constitution protects a very limited number of rights. The fact that the right to bear arms is one of them shows that this is an important right. We should not go against this, particularly since the possession of weapons helps keep us (so the argument goes) safe from the possibility of government tyranny.
We can also argue that we need guns so that we can protect ourselves and our families. Criminals all over the US have guns. If we do not let law-abiding people have guns, we put them at a disadvantage and make them easier prey for criminals.
Uy...if I have to:
The Constitution of the United States allows for it, therefore it is simply one's right to own a gun.
If we are not permitted to own a gun ourselves, government has a monopoly on coercive force, and they can use that force to repress the ordinary citizen.
We have a right to self-protection, and owning a gun is simply a part of protecting ourselves.
Cars, it could be argued, are just as dangerous, and kill people just as easily, perhaps even more frequently than gun-use. So, if I can own a car, why can't I own another thing that could potentially kill someone?
I'm not getting a license to kill someone, I'm simply getting a license to own a gun. In fact, the gun could have no bullets.
That's all I can think of for now. But I'd say each argument is flawed.