I suppose to understand the second amendment fully I would have to have read James Madison's other writings to see how he commonly structured his sentences. That stated, I think what Madison may have been saying is not that the people bear arms because the people are the militia, but because the people are NOT the militia.
The purpose of the constitution in general and the bill of rights in particular was to limit the power of government. To that end, he had to acknowledge the need for security of a free state while at the same time assuring the people that this militia would not and could not be used to tyrannize the people. He therefore chose the phrase 'well regulated' in describing the militia.continued: