A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.
The part you’re misreading here is
A well regulated Militia, being necessary to the security of a free State, <- COMMA, the right of the people to keep and bear Arms, shall not be infringed.
So what’s being said here is, the right of the people to keep a well regulated militia AND to privately own arms individually, to ensure the former, shall not be infringed on either level.
