Obviously no one denied that individuals make up the "class" that is referred to by the term "people" in the Constitution. (And, BTW, it isn't only citizens that the term "people" refers to.)
This is where logic fails you. Obviously the rights noted in the Ninth Amendment do not "extend" to any individual. The Ninth Amendment identifies rights that belong only to "the people" as a whole.
Likewise, again, to interpret the term "the right of the people" in the Second Amendment as "the rights of individuals" makes the first clause of the sentence nonsensical. You haven't yet made sense of that prefatory clause. (Neither did Scalia.)
Let me get this straight.
Let us define people as set A. Now A={x|x is a citizen of the U.S}
a is a subset of A.
You think that something that applies to all A does not apply to a?
I don't think my logic is faulty my friend.
I suppose there is a way to argue for emergent properties or something of the like. But one would use language that indicates one is talking about A iff A is complete.
For instance, if we take A={x|x is prime}
We could say that All A have the property of only being divisible by one and their self. For no subset of A will this be false.
Now, we could say that A is an infinite set. In that case we can clearly see that it is possible for some subsets of A to not have this quality. However, the language we use refers to a property of the set as a whole. The phrase keep and bear arms would make no sense if it were applied to the set only as a whole and not a property that is true of members of the set.
Rather, the right would read, for the people, the right to arms shall not be infringed.
The difference is subtle, but when one is talking about a right that applies to a class as a whole and not members of the class, the language would specify such.
The interpretation of this right to individuals does not make the prefatory clause nonsensical. A militia is a subset of set A. The idea that all members of set A have this right, enables the purpose (not limiting) of the prefatoy clause to be actualized.
The militia is a subset of A, formed or existing of their own accord. No government has the authority to establish a militia, only to regulate, call upon, and discipline. So, the people have the right to establish a militia (not states because that would be too close to a standing army). So, individuals must have the right to keep and bear arms separate from the government, in order to actualize a militia.
The reason for a militia is self defense. I am not one of those who thinks that this self defense was to be against our government because if such a need arose, the constitution would be void and we would have no government (as the constitution provides peaceful ways to change government). However, threats, both foreign and domestic can arise. And such is the purpose for the militia. Now, that individuals have the right for this purpose to keep and bear arms, we should turn to the question of whether that right should be limited to only militia activity. The answer is no. Self defense is fundamental to our founding, to our constitution, and to the second amendment. So, to read the amendment in such a way as to drive a wedge between the purpose of the second amendment (self defense) and the entity it preserves (the militia) is shocking. The right belongs to the people not to members of the militia.
In short, the preservation of the militia for self defense, through reservation of the right to keep and bear arms by the people, contains in it the purpose of self defense of those persons, even when not directly connected to militia activity.