The right is to bear arms in order to form a militia, according to the second amendment. The second amendment does not explicitly enumerate the right to shoot someone with it or defend oneself, nor does it mention these as reasons why we have a right to bear arms, although Judiciary findings have supported the right to defend oneself with a gun.
We do have the right, but it is not given to us by the second amendment. The only thing that is given to us by it is the right to bear arms, which is different than the right to use them. Much in the same way that simply saying we have a right to bear arms does not afford us the right to shoot whomever we want with it. The interpretation of legal uses is not mentioned in the second amendment, except as a means of keeping an armed militia.
Secondly, there are many cases where we do NOT have a right to defend ourselves with a gun (or rather, by shooting a gun).