WHY DO WE HAVE THE RIGHT TO BEAR ARMS?

In part because the Founders saw standing armies as potential threats to liberty and felt that citizen-soldiers in a militia would be an effective counter-balance. From The Right to Bear Arms by Robert J. Spitzer, pp. 27-28:

To judge by the brief debate about and modest wording changes in the amendment's four versions quoted here, the basic sentiment was held throughout - that citizens have a constitutionally protected right to serve in militias when called into service by, and in defense of, state and country. The aim was to ensure the continued existence of state militias as a military and political supplement and counterbalance to the national army and more broadly to national power (Wills, 1999).

In essence, the 2nd Amendment was..

a political compromise between politically popular and state-controlled militias and a politically unpopular but militarily necessary national professional army.

Thomas Jefferson wrote several times about the danger of having a standing army:

"There are instruments so dangerous to the rights of the nation and which place them so totally at the mercy of their governors that those governors, whether legislative or executive, should be restrained from keeping such instruments on foot but in well-defined cases. Such an instrument is a standing army." --Thomas Jefferson to David Humphreys, 1789. ME 7:323

"I do not like [in the new Federal Constitution] the omission of a Bill of Rights providing clearly and without the aid of sophisms for... protection against standing armies." --Thomas Jefferson to James Madison, 1787. ME 6:387

"Standing armies [are] inconsistent with [a people's] freedom and subversive of their quiet." --Thomas Jefferson: Reply to Lord North's Proposition, 1775. Papers 1:231