The reason is that a right to property would not distinguish between owning a rocket launcher or a handgun, because in principle both are held as property . On the other hand, the right to self-defense does clearly delimit what types of weapons an individual may own within civilized society. Nonetheless, why it is valid to own a handgun, and not a tank or howitzer, is not self-evident. This issue is what I'll address next. Beyond the obvious methodological problem of rationalism, this argument represents a serious misunderstanding of the right to self-defense, and the action that this right sanctions.
Rights are moral principles sanctioning man's freedom of action in a social context.
The right to self-defense sanctions only those actions you take at the moment a crime occurs. However, if you take the punishment of the criminal into your own hands subsequent to a crime, then you are a vigilante. With respect to self-defense, the law requires that your action is commensurate with the crime committed against you. For instance, you cannot pull out a shotgun and shoot a man for simply grabbing an orange out of your backpack in the park. You do have the right, however, to chase him down and hold him until the authorities arrive, or to enlist others in your attempt to stop him.