The founding fathers envisioned two possible futures: (1) a federal government so small that it would be unable to garner the resources to defend itself, and (2) a federal government so large that it had a standing army large enough to defend itself. In either case, it made sense to have an armed citizenry. In the first case to defend the country, and in the second case to defend the citizenry against the possibility of the military being used against it.
Thats it in a nutshell.
The
security of a free State depends on being able to defend itself from outside threats, but at the same time to be able to defend itself from those who would take it over from within, using the standing army (and destroy that freedom).
The sentiment was that the vast number of citizens, by force of arms if necessary, would so overwhelm the standing army in the event of the latter scenario, that even in the absence of military training, the citizens would prevail and retain their freedom.
In the event for a foreign threat, those same citizens could augment the Military, and by virtue of being familiar with arms, be more easily trained to enter those ranks.
For freedom, this was seen as a win/win, no matter which way events transpired, and in the event neither was necessary, no harm was done. Ours is an armed tradition.