That's an interesting argument, but it is flawed.
1) "Humans (its easier to talk about humans rather than men to avoid confusion) exist," and
2) "Humanity exists"
do not have the exact same meaning, (even though I agree with you that the method of proving each is the same).
Formally, I believe the distinction is as follows:
1) There exists at least one x which is an instance of Humanity.
2) There exists at least one x which is Humanity.
I believe that your (and I think Rand's) mistake is that you are literally identifying Humanity with its instances. That's nonsensical because you are treating a noun and a predicate as though they were identical.
The reason you are making this error is because you are failing to differentiate between a relation of identity and a relation of definition.
I think it is correct (and I think you would agree) to say that
3) An abstraction x exists if and only if there exists at least one particular y such that y is an instance of x.
This statement is a definition of the existence of abstractions. Thus, there is a material equivalence between 1) and 2) but no logical equivalence. It is important to make this distinction.
Another way of explaining this error is like this.
First, if two things A and B are identical, then the existence of one necessarily entails the existence of the other.
However, one cannot flip this statement and say that because the existence of A necessarily implies the existence of B and vice versa, that therefore A is B.
An obvious counterexample here is that the existence of the number 1 necessarily entails the existence of the number 2, and vice versa, but that does not mean that 1 is 2.
I think you are jumping to conclusions. Saying that man is an abstraction no more implies that he is only an abstraction than saying that John is tall implies that John is characterized only by tallness.