The second amendment tells us its purpose. “A well regulated Militia, being necessary to the security of a free State…”
It was not to hunt and it was not even specifically for individual self defense. It was for the defense of society against all those who would dismantle a free state. The militia, for all intensive purposes, at the time of the writing was the military but made up of every male civilian with a gun. (over generalization but you get my point)
The second amendment was there for individuals and groups to protect their freedom. This would include the right to life and self protection. To restrict the second amendment to a set of weapons inferior to set of weapons used by the state is, in a way, the restriction of the ability of individuals to protect their freedoms from the institution that has, throughout history, been the greatest destroyer of freedom and liberty.