The original text:
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.
There are two sets of citizens discussed in the Second Amendment.
One group is the set of ALL citizens, named "the People."
The other set is those who bear arms in the service of the government. This includes armed police officers, National Guardsmen, Sheriffs, FBI agents etc. They are named "the militia." It seems crystal clear to me that the militia and the people are two different groups. When the Constitution is written there are no public police forces -- policing is usually a soldiers job.
2A states that that in order for a State to be secure in it's freedom, the militia cannot be out of control -- they must be regulated. The only check (regulation) on the militia is to make sure that the People have the ability to confront the militia. They can of course do this through laws -- but since the militia is charged with enforcing the laws, to whom can the People turn when the militia is breaking the laws?
The people must be able to defend themselves against the militia with force and confront the militia with force. And since the militia is armed by definition, to ensure the People can perform this regulatory function, the right of the People to keep and bear arms shall not be infringed.