Nicomachean Ethics II.6b

If it is thus, then, that every art does its work well- by looking to the intermediate and judging its works by this standard (so that we often say of good works of art that it is not possible either to take away or to add anything, implying that excess and defect destroy the goodness of works of art, while the mean preserves it; and good artists, as we say, look to this in their work), and if, further, virtue is more exact and better than any art, as nature also is, then virtue must have the quality of aiming at the intermediate.

That's a long deduction with two questionable assumptions.  (A) IF every art does its work well by creating works that can't be improved either by adding or taking away; (B) AND IF virtue is more exact and better than any art (as nature is); (C) THEN virtue must have the quality of aiming at this intermediate point of balance.

So A∧B⊃C, for those of you who want to study philosophy formally. Or, you can put it this way: 

(Assumption) A
(Assumption) B
∴ C

The deduction follows if the assumptions are true. Are they true? 

It isn't clear to me that the first assumption is true. In The Singer of Tales, Albert Lord demonstrates that much of the heroic poetry of the Homeric tradition was oral by nature, and part of a performance was to edit it to fit the audience's interest level and available time. For that audience, such a shortening or stretching improved the work; but arguably no such work was an actual improvement over Homer's version. These are of course two different works, and one could argue that each performance has to hit the right balancing point ("intermediate" or "mean") for its audience. However, one can also admit that there is nothing wrong with Homer's work -- that's why it has endured for millennia -- even though it could be improved for a particular audience by editing it (or even stretching it, although it's already quite long). 

The second assumption turns on an important ambiguity in what it means to be 'better than.' Aristotle says here that nature is better than any art; and in Physics II and elsewhere, he says that 'art imitates nature.' However, as we have already discussed, art has a crucial role in perfecting the flaws found in nature, as by improving eyesight when the natural eye is weak. If art can perfect nature, it can't be 'less good' because you perfect something by bringing it to a greater good than it had by itself. 

I suspect this means that 'good' is being used in two senses here. Nature is the source of everything to which we might apply an art, and creates the basic things that our arts can only improve upon but not make from nothing. In that sense, nature is higher and better than art. Yet art must have a 'good' to offer insofar as it is being applied; and that good is based upon the ability of us to understand the reasoning behind the created thing (telos) so that we can intuit how to improve it. 

Given the structure of the deduction, if either of the assumptions are false, the deduction fails. That doesn't mean the conclusion is false; it just means that the logic itself cannot guarantee the truth of the conclusion. 

I mean moral virtue; for it is this that is concerned with passions and actions, and in these there is excess, defect, and the intermediate. For instance, both fear and confidence and appetite and anger and pity and in general pleasure and pain may be felt both too much and too little, and in both cases not well; but to feel them at the right times, with reference to the right objects, towards the right people, with the right motive, and in the right way, is what is both intermediate and best, and this is characteristic of virtue. Similarly with regard to actions also there is excess, defect, and the intermediate. Now virtue is concerned with passions and actions, in which excess is a form of failure, and so is defect, while the intermediate is praised and is a form of success; and being praised and being successful are both characteristics of virtue. Therefore virtue is a kind of mean, since, as we have seen, it aims at what is intermediate.

Again, it is possible to fail in many ways (for evil belongs to the class of the unlimited, as the Pythagoreans conjectured, and good to that of the limited), while to succeed is possible only in one way (for which reason also one is easy and the other difficult- to miss the mark easy, to hit it difficult); for these reasons also, then, excess and defect are characteristic of vice, and the mean of virtue;

For men are good in but one way, but bad in many.

Aristotle's understanding of what he sometimes calls "the so-called Pythagoreans" is helpfully explained here.

Virtue, then, is a state of character concerned with choice, lying in a mean, i.e. the mean relative to us, this being determined by a rational principle, and by that principle by which the man of practical wisdom would determine it. Now it is a mean between two vices,* that which depends on excess and that which depends on defect; and again it is a mean because the vices respectively fall short of or exceed what is right in both passions and actions, while virtue both finds and chooses that which is intermediate. Hence in respect of its substance and the definition which states its essence virtue is a mean, with regard to what is best and right an extreme.

* Or three, or more; when we get to courage you will see that he has two different defects on the excess side of the ledger. 

But not every action nor every passion admits of a mean; for some have names that already imply badness, e.g. spite, shamelessness, envy, and in the case of actions adultery, theft, murder; for all of these and suchlike things imply by their names that they are themselves bad, and not the excesses or deficiencies of them. It is not possible, then, ever to be right with regard to them; one must always be wrong. Nor does goodness or badness with regard to such things depend on committing adultery with the right woman, at the right time, and in the right way, but simply to do any of them is to go wrong.

There is no virtuous way to commit adultery, then; and he mentions murder as well. It's worth thinking about all those 'would you go back to kill Hitler' thought experiments, then. The only reason to consider such a thing (were it possible) is that it might be virtuous; here we are told there can be no right way to do it.  

It would be equally absurd, then, to expect that in unjust, cowardly, and voluptuous action there should be a mean, an excess, and a deficiency; for at that rate there would be a mean of excess and of deficiency, an excess of excess, and a deficiency of deficiency.

This is a very Aristotelian point.  

But as there is no excess and deficiency of temperance and courage because what is intermediate is in a sense an extreme, so too of the actions we have mentioned there is no mean nor any excess and deficiency, but however they are done they are wrong; for in general there is neither a mean of excess and deficiency, nor excess and deficiency of a mean.

All of that will become clearer once we get to the examples of specific virtues.