We also have to understand some context. There was a serious effort for the USA not to have a military. It was envisioned that state militias could be called up from amongst the masses. Eventually the Army and Navy were incorporated into the Constitution (Article 1)**, but the anti-federalists -fearing a powerful federal government- then envisioned states being able to raise a militia to oppose -if necessary- the federal.

Which was the other major prong of the Heller Court's reasoning. They also viewed the 2A as serving as a bulwark against the federal government neutralizing the state militia in order to accrete to itself a monopoly on armed power. The Founders were keenly against the idea of the only army being the one controlled by the new President - they generally didn't want the President to have a standing army at his command, and didn't want the States to be without their own armies (at need). Subject to the caveat (which we should always keep in mind) that there were minority viewpoints on that subject among the Founders - Washington, for example, was a believer in having a (small) standing army:

press-pubs.uchicago.edu: Article 1, Section 8, Clause 12: George Washington, Sentiments on a Peace Establishment

Anyway, Scalia's argument is that if the federal government has the power to disarm the citizen's militia, it would effectively destroy the citizen's militia - which outcome the 2A intends to prevent. For the citizen's militia to have meaningful existence, its members have to have access to firearms and be reasonably conversant with their use - which can only happen if they have the individual right to own firearms. The citizen's militia consists of all adult citizens. Therefore, the federal government can't prohibit individual citizens from owning firearms.