As silly as this argument may be, how foolish would I be if I could not logically debate such nonsense? Here is my attempt:
Rights are derived from equality, freedom, responsibility, and property. For example you have the right to defend YOUR body with YOUR gun so long as you don't violate the rights of others by harming them or their freedom in some way, and you are responsible enough to own a gun. By responsibility I mean if you don't grasp the concept of death because you're incompetent or too young, you probably shouldn't have a gun. Or if you have the tendency to rob people every time you hold a gun, you don't have the responsibility (not to mention this is also a violation of their rights).
Simply possessing a nuclear weapon does no one any harm. However, a nuclear weapon has exactly two uses - to destroy a large area, or to be something cool to keep in your garage and show your friends. This makes it useless for self defense, unless you're defending yourself against an entire country, which I think the federal government can take care of better than myself, as scary as trusting them is. You would have no use for a nuclear weapon to protect our contry from domestic aggressors (the federal government), as how would you use it against them without destroying millions of citizens who live peacefully? While you can own something if you want, so long as you don't misuse it, your desire to own a nuclear weapon is of fairly low importance to me. On the other hand, if you decide to go a little crazy, there are dire consequences. The constitution mentions "common defense" twice: once in the preamble and once in article 1, I think it's section 8... whatever the one is where congress' powers are enumerated. A single nuclear arm is a great threat to the common defense of the nation. Do you see here then why it's not your right to own a nuclear weapon? People have the right to live safely. If you don't use the nuke, no one is harmed - but is it prudent to trust hundreds of millions of lives so that one man can pursue his weapons hobby?
Anti's may argue that a single firearm can also do great damage, while your desire to shoot for recreation is of little importance to them. However, a gun is useful for defense. Personal, domestic, foreign. And guns are a good balance of power as they cannot be used by one man to devastate a nation, but they can be used by the masses to resist tyrannies. No single soldier in the military is trusted with nuclear arms, either. Guns can serve to protect the nation, nuclear arms can serve to destroy it. Somewhere in the middle of the two is a hazy line that you can deal with. But I'd like to see you hit a bad guy with a nuke and not harm any bystanders.
Note that so far I've demonstrated the imprudence of trusting you with a nuke, but have only hinted as to why it's not your right. Remember what I said about equality? The basic premise is all men and women are created equal. That means we all have the same rights, including self defense. How can I defend myself and my family against you, the man with an A-bomb? Even if I have one myself, I am vulnerable. Even if I have an army of a million men, I am defenseless against you. This is not equality. I am not your slave. I own my own body, and may protect it. It is not your right.