There are a few ways to argue against the "only for the Militia" claim with the 2nd amendment.
#1 - Change the quote up and replace words like below:
A well educated citizenry [regulated Militia], being necessary to the security of a free State, the right of the people to keep and read books [bear Arms], shall not be infringed.
You would never argue that only "educated citizenry" are allowed to keep and read books... it is obvious that all people have the right to keep and read books SO THAT we can have an educated citizenry. In the same way, we have the right to keep and bear arms SO THAT we will have a well regulated Militia. (Regulated didn't mean then, what it means now. It basically meant "in good working order." https://web.archive.org/web/20180201191936/http://www.constitution.org/cons/wellregu.htm)
Or again... "A well balanced breakfast being necessary to the start of a healthy day, the right of the people to keep and eat food shall not be infringed."
You would never say that the right to keep and eat food is based on eating a well balanced breakfast or that it is the well balanced breakfast that has a right to keep and eat food. It is clear that in order to be able to have a well balanced breakfast, the people need to be able to keep and eat food.
In the same way, the "right of the people" is not dependent upon the "well regulated militia." A well regulated militia is only possible when the people have the right to keep and bear arms.
Here you can see what an English expert has to say about it:
https://web.archive.org/web/20170720100107/http://www.constitution.org:80/2ll/schol/2amd_grammar.htm
Here is a good image showing the breakdown of the sentence:
http://www.libertygunrights.com/2-A_Meaning_pg2.gif
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#2 - Read the Federalist Papers. The Federalist Papers were written by writers and supporters of the Constitution, to explain to the people why they should ratify the Constitution.
They essentially define the term militia as the founders understood it.
"Let a regular army, fully equal to the resources of the country, be formed; and let it be entirely at the devotion of the federal government; still it would not be going too far to say, that the State governments, with the people on their side, would be able to repel the danger. The highest number to which, according to the best computation, a standing army can be carried in any country, does not exceed one hundredth part of the whole number of souls; or one twenty-fifth part of the number able to bear arms. This proportion would not yield, in the United States, an army of more than twenty-five or thirty thousand men. To these would be opposed a militia amounting to near half a million of citizens with arms in their hands, officered by men chosen from among themselves, fighting for their common liberties, and united and conducted by governments possessing their affections and confidence. It may well be doubted, whether a militia thus circumstanced could ever be conquered by such a proportion of regular troops."
According to census in 1790, there were 807,094 free white males 16+, of which 1/25th is 32,283.
According to census in 1790, there were 3,893,635 total population, of which 1/100th is 38,936.
Both are right around "an army of more than twenty-five or thirty thousand men." He then says "To these would be opposed a militia amounting to near half a million of citizens" which is really close to "all males 16+" amount (807,094).
These numbers aren't perfect, because the first census was taken in 1790, but not released until 1791. This federalist paper was written January 29, 1788.
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#3 - Recent Judicial Rulings state the 2nd amendment is an individual right, just like all the other amendments in the Bill of Rights
District of Columbia v. Heller, 554 U.S. 570 (2008), is a landmark case in which the Supreme Court of the United States held, in a 5–4 decision, that the Second Amendment protects an individual's right to possess a firearm unconnected with service in a militia for traditionally lawful purposes, such as self-defense within the home
https://en.wikipedia.org/wiki/District_of_Columbia_v._Heller
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#4 - It's copied in almost every other constitution with the same exact meaning and interpretation. There are only 6 states without a state constitutional right to keep and bear arms.
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#5 - You can read other "drafts" of the amendment to see what the intent was:
https://en.wikiquote.org/wiki/Second_Amendment_to_the_United_States_Constitution
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#6 - Current US Code defines the term militia as all able-bodied males 17-44.
U.S. Code › Title 10 › Subtitle A › Part I › Chapter 12 › § 246
10 U.S. Code § 246 - Militia: composition and classes
(a) The militia of the United States consists of all able-bodied males at least 17 years of age and, except as provided in section 313 of title 32, under 45 years of age who are, or who have made a declaration of intention to become, citizens of the United States and of female citizens of the United States who are members of the National Guard.
(b) The classes of the militia are—
(1) the organized militia, which consists of the National Guard and the Naval Militia; and
(2) the unorganized militia, which consists of the members of the militia who are not members of the National Guard or the Naval Militia.
(Aug. 10, 1956, ch. 1041, 70A Stat. 14, § 311; Pub. L. 85–861, § 1(7), Sept. 2, 1958, 72 Stat. 1439; Pub. L. 103–160, div. A, title V, § 524(a), Nov. 30, 1993, 107 Stat. 1656; renumbered § 246, Pub. L. 114–328, div. A, title XII, § 1241(a)(2), Dec. 23, 2016, 130 Stat. 2497.)
https://www.law.cornell.edu/uscode/text/10/246
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#7 - Current US Code says States have the authority to appoint officers and train the militia, therefore it cannot be used to be interpreted as a "federal military" such as the National Guard.
In Article I Section 8 of Constitution of the United States the power of congress to organize the militia is described:
To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;
To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress;
https://www.usconstitution.net/xconst_A1Sec8.html
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