First I just want to gather together some of what we had discussed in comments:
- Your question seems to me to be basically one about Aristotle's idea of catharsis; note that this theory itself is responding to Plato's "indictment" of poetry and drama as dangerous influences on people's minds, because they inspire empathy with often violent and/or criminal dramatic personae. (Plato famously bans poets and actors from his Republic.)
- In the passage we're discussing Nietzsche is talking about Christianity as a "religion of pity"; he is analyzing the affect of pity through a complex and subtle psychology of morality.
- Gutenberg's copy of the text is here; the excerpt in question is from section 7.
As the section is not really that long (~500 words); and since I've tried to argue before for having as much context as reasonably possible when discussing Nietzsche, I reproduce the section in its entirety below (with my emphasis and some commentary interspersed):
Christianity is called the religion of pity.—Pity stands in opposition to all the tonic passions that augment the energy of the feeling of aliveness: it is a depressant. A man loses power when he pities. Through pity that drain upon strength which suffering works is multiplied a thousandfold. Suffering is made contagious by pity; under certain circumstances it may lead to a total sacrifice of life and living energy—a loss out of all proportion to the magnitude of the cause (—the case of the death of the Nazarene).
Pity weakens through multiplying "reactive" passions, melancholy and woe and the entire 'negative' spectrum of affects. (I believe this argument is perhaps in itself not original to Nietzsche.) He explains Christ's sacrifice as a suicidal melancholy eruption of a kind of pity 'virus', one which perhaps betrays a kind of nihilism.
It may be interesting to note how he emphasizes this "viral" and contagious nature of pity; which seems still basically in line, however, with the problem of the "multiplication" of suffering that pity causes, perhaps even an extrapolation: pity is an outbreak of the violence of the negative, which if taken far enough can become turned entirely against life, even self-destructive. Christ as the "Typhoid Mary" of a strange virus of bitterness, misery and resentment; this "pity" has turned the world into a madhouse.
This is the first view of it; there is, however, a still more important one. If one measures the effects of pity by the gravity of the reactions it sets up, its character as a menace to life appears in a much clearer light. Pity thwarts the whole law of evolution, which is the law of natural selection. It preserves whatever is ripe for destruction; it fights on the side of those disinherited and condemned by life; by maintaining life in so many of the botched of all kinds, it gives life itself a gloomy and dubious aspect. Mankind has ventured to call pity a virtue (—in every superior moral system it appears as a weakness—); going still further, it has been called the virtue, the source and foundation of all other virtues—but let us always bear in mind that this was from the standpoint of a philosophy that was nihilistic, and upon whose shield the denial of life was inscribed.
Behind this simple critique of morality on the "pragmatic" basis of not multiplying suffering beyond necessity, Nietzsche wants to argue for a larger world-historical or even universal-historical sense of pity. He argues that at this level of 'higher' politics pity is essentially life-denying, and a weakness for any "higher" morality. He notes that pity has been called the highest virtue, the "essence" of virtue; and wants us to bear in mind that such assertions of pity's ascendancy in the realm of virtue may conceal a basically nihilistic impulse. He will try to clarify some of this through the example of Schopenhauer, who also makes this basic claim that pity is a means by which life denies itself (though perhaps without Nietzsche's critical eye for civilizational diagnosis):
Schopenhauer was right in this: that by means of pity life is denied, and made worthy of denial—pity is the technic of nihilism. Let me repeat: this depressing and contagious instinct stands against all those instincts which work for the preservation and enhancement of life: in the rôle of protector of the miserable, it is a prime agent in the promotion of décadence—pity persuades to extinction.... Of course, one doesn’t say “extinction”: one says “the other world,” or “God,” or “the true life,” or Nirvana, salvation, blessedness.... This innocent rhetoric, from the realm of religious-ethical balderdash, appears a good deal less innocent when one reflects upon the tendency that it conceals beneath sublime words: the tendency to destroy life. Schopenhauer was hostile to life: that is why pity appeared to him as a virtue....
Pity is a virtue for those animated by hostility towards life -- much moralizing rhetoric is less innocent than it appears when it hallows pity with beautiful words. Schopenhauer's elevation of pity in particular betrays this nihilistic tendency, or thirst for extinction.
Now we come to the portion with which we are especially concerned:
Aristotle, as every one knows, saw in pity a sickly and dangerous state of mind, the remedy for which was an occasional purgative: he regarded tragedy as that purgative. The instinct of life should prompt us to seek some means of puncturing any such pathological and dangerous accumulation of pity as that appearing in Schopenhauer’s case (and also, alack, in that of our whole literary décadence, from St. Petersburg to Paris, from Tolstoi to Wagner), that it may burst and be discharged.... Nothing is more unhealthy, amid all our unhealthy modernism, than Christian pity. To be the doctors here, to be unmerciful here, to wield the knife here—all this is our business, all this is our sort of humanity, by this sign we are philosophers, we Hyperboreans!—
For some context, I want to note that Aristotle's assertions in the poetics about catharsis "releasing" the dangerous pities and fears aroused by tragedy are in the larger context of the value of drama and verse, the problem of empathy with 'dangerous' impulses that may be dramatized by playwrights or versified by poets. Nietzsche is noting that in making such a claim about catharsis, Aristotle is conceding his basic point that pity is as viral and dangerous an emotion as fear -- perhaps especially for crowds.
Nietzsche goes on to say, as it were asserting Aristotle against Schopenhauer, that the instinct of life would precisely prompt us to "puncture" dense concentrations of pity and discharge them, releasing the tension and danger that have accumulated. But the problem, of course, is identifying and isolating such pathological distortions in the first place -- seeing beyond the surface to what Nietzsche calls 'our sort' of humanity. He says this seeing-beyond (or perhaps we can say "looking-down") is the sign by which philosophers recognize one another in the last instance.
