It makes more sense if you read the original draft of the 2A:
The right of the people to keep and bear arms shall not be infringed; a well armed and well regulated militia being the best security of a free country: but no person religiously scrupulous of bearing arms shall be compelled to render military service in person.
1) The PEOPLE have the right to keep and bear arms.
2) A well armed was the best security of a free country, BUT
2.a) No-one whose religion forbid bearing arms could be forced to serve in the militia
And here is the second draft:
A well regulated militia, composed of the body of the People, being the best security of a free State,
the right of the People to keep and bear arms, shall not be infringed, but no one religiously scrupulous of bearing arms, shall be compelled to render military service in person.
The Amendment would take what would become its final form in the Senate, where the religious-objector clause was finally removed and several other phrases were modified. For instance, the phrase referencing the militia as "composed of the body of the People" was struck, and the descriptor of the militia as "the best security of a free State" was modified to "necessary to the security of a free State".
Several other changes were proposed and rejected, including adding limitations on a standing army "in time of peace" and adding next to the words "bear arms" the phrase "for the common defence".
So, the Senate specifically rejected the addition of "for the common defense" because the 2A protects an INDIVIDUAL RIGHT.
Edit to add source: