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Yes, it is sometimes said in Mahayana that "hinayana" is the basic foundation, and that its primary focus is to learn to be satisfied with little, to control one's desire for entertainment, lust for sensual pleasures, and impulse to grasp after objects of the world. The end goal of this phase is an image of someone like a warrior or an ascetic: cool, detached, dispassionate, controlled.
And then, on the next level (confusingly called "mahayana" - same as the broad name referring to all non-conservative schools), the practice shifts from overcoming desires to overcoming aversion towards the people and the world.
It is recognized that someone at the hinayana level may develop a tendency to avoid dealing with people and the world because many of these interactions often lead to disturbance and drama, and away from what would otherwise be self-contained peace. Someone like that may have a rather strong aversion to real-life issues, anything "spiritually dirty", and especially to "lowly humans" with their constant self-generated trouble.
In order to overcome that, the mahayana practice is to go out to the world and learn to deal with its issues, while still keeping one's balance and avoiding any sense of egotistic pride that would come from one's "spiritual superiority". This is called "the bodhisattva practice", to basically leave all Dharma-Theory home and dive into the world, while learning to be authentic and helpful. The end result of this is an image of someone very warm, strong, and open, who has enough inner power and confidence that he or she can be very down-to-earth, very real, without formalities and artificial boundaries that come from fear. This is very different from the aloof ascetic image cultivated on the previous stage. It is someone very warm and very real.
So that's what I meant when I said that in Mahayana the focus shifts from desires to aversion.
Now, regarding that idea of breaking taboos - that comes at the vajrayana level. That is where the practice transcends dharma that can be explained / formalized as rules, and gets into dharma that is felt and intuitively improvised like a dance. In order to get there, one must study the edge cases where the superficial and the authentic understanding of dharma come in conflict. This is when controversial practices like burning buddhist texts, getting intoxicated, stealing something, hurting someone, or engaging into adultery may be prescribed. Yes, it is correct to say that these practices are performed with the goal of overcoming one's deep-lying attachments. It is never the case that all rules are simply lifted and the student can do anything, not at all. Instead, the student, working under the guidance of his long-time mentor, practices on overcoming his or her strongest phobia, strongest attachment, in the most effective way possible, while minimizing damage to the other (worldly) side, and hopefully even providing them with some long-term benefit as well. That's quintessentially vajrayana-level practice, not mahayana-level.
Anyway, coming back to Mahayana,
OP: If nibbida is meant as an antidote to lobha then is there a corresponding antidote to dosa? Or should nibbida be an antidote to both?
Since now we know we are talking specifically about dosa-towards-the-world-and-people, it becomes clear that a key antidote to that is compassion, as well as the four brahmaviharas in general. The practices of metta meditation, of tonglen meditation, and of dedicating the virtue to all sentient beings before and after each formal practice session are all examples to antidotes to aversion. The Mahayana paramita of Patience is essentially about overcoming aversion, too. The Bodhisattva's vow to defer entering Nirvana until all sentient beings are liberated is an antidote to aversion towards Samsara at large.
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It's not accurate that the suttas do not address aversion (dosa) and the antidote for it.
For example, in the Nakulapita Sutta, the Buddha advises householder Nakulapita with regards to his aversion to old age and disease:
Then the householder Nakulapita went to the Blessed One and on arrival, having bowed down to him, sat to one side. As he was sitting there he said to the Blessed One, "Lord, I am a feeble old man, aged, advanced in years, having come to the last stage of life. I am afflicted in body & ailing with every moment. And it is only rarely that I get to see the Blessed One & the monks who nourish the heart. May the Blessed One teach me, may the Blessed One instruct me, for my long-term benefit & happiness."
"So it is, householder. So it is. The body is afflicted, weak, & encumbered. For who, looking after this body, would claim even a moment of true health, except through sheer foolishness? So you should train yourself: 'Even though I may be afflicted in body, my mind will be unafflicted.' That is how you should train yourself."
Later, Ven. Sariputta explained this in more detail to Nakulapita, which incidentally provides the antidote for aversion (dosa) through the contemplation of not-self (anatta):
"And how is one afflicted in body but unafflicted in mind? There is the case where a well-instructed disciple of the noble ones — who has regard for noble ones, is well-versed & disciplined in their Dhamma; who has regard for men of integrity, is well-versed & disciplined in their Dhamma — does not assume form to be the self, or the self as possessing form, or form as in the self, or the self as in form. He is not seized with the idea that 'I am form' or 'Form is mine.' As he is not seized with these ideas, his form changes & alters, but he does not fall into sorrow, lamentation, pain, distress, or despair over its change & alteration.
"He does not assume feeling to be the self...
"He does not assume perception to be the self...
"He does not assume fabrications to be the self...
"He does not assume consciousness to be the self, or the self as possessing consciousness, or consciousness as in the self, or the self as in consciousness. He is not seized with the idea that 'I am consciousness' or 'Consciousness is mine.' As he is not seized with these ideas, his consciousness changes & alters, but he does not fall into sorrow, lamentation, pain, distress, or despair over its change & alteration.
"This, householder, is how one is afflicted in body but unafflicted in mind."
When the Buddha visited the sick ward of monks in Gelañña Sutta, he advised the contemplation of impermanence (anicca), which also works as an antidote for aversion (dosa):
"Sensing a feeling of pleasure, he discerns that it is inconstant, not grasped at, not relished. Sensing a feeling of pain... Sensing a feeling of neither-pleasure-nor-pain, he discerns that it is inconstant, not grasped at, not relished. Sensing a feeling of pleasure, he senses it disjoined from it. Sensing a feeling of pain... Sensing a feeling of neither-pleasure-nor-pain, he senses it disjoined from it. When sensing a feeling limited to the body, he discerns that 'I am sensing a feeling limited to the body.' When sensing a feeling limited to life, he discerns that 'I am sensing a feeling limited to life.' He discerns that 'With the break-up of the body, after the termination of life, all that is sensed, not being relished, will grow cold right here.'
"Just as an oil lamp burns in dependence on oil & wick; and from the termination of the oil & wick — and from not being provided any other sustenance — it goes out unnourished; in the same way, when sensing a feeling limited to the body, he discerns that 'I am sensing a feeling limited to the body.' When sensing a feeling limited to life, he discerns that 'I am sensing a feeling limited to life.' He discerns that 'With the break-up of the body, after the termination of life, all that is sensed, not being relished, will grow cold right here.'"
OP: [comment] I was hoping that this topic would be more about choosing or failing to do what one is or feels averse to -- to some extent Nakulapita's growing old wasn't a choice (extent to the extent of choosing to identify with form, feeling, etc.).
In Vajjiputta Sutta (quoted below), the monk alone in the forest, heard music and festivities in a neighbouring village, and felt aversion towards his seclusion (which is considered good for monks by the Dhamma). This is an aversion by choice (unlike disease and old age), which was overcome by changing his perspective or changing his view of the situation.
On one occasion a certain monk, a Vajjian princeling, was dwelling near Vesali in a forest thicket. And on that occasion an all-night festival was being held in Vesali. The monk — lamenting as he heard the resounding din of wind music, string music, & gongs coming from Vesali, on that occasion recited this verse:
I live in the wilderness all alone
like a log cast away in the forest.
On a night like this,
who could there be
more miserable than me?Then the devata inhabiting the forest thicket, feeling sympathy for the monk, desiring his benefit, desiring to bring him to his senses, approached him and addressed him with this verse:
As you live in the wilderness all alone
like a log cast away in the forest,
many are those who envy you,
as hell-beings do,
those headed for heaven.The monk, chastened by the devata, came to his senses.
I agree with Andrei: In this answer, by understanding the underlying reasons for others' sufferings, we can generate compassion towards them. This was proposed as an antidote towards contempt. This is one example of overcoming aversion by changing one's perspective or view of a situation.
In fact, disgust (nibbida) to cure passion (lobha), compassion to cure contempt, not-self or impermanence to cure aversion towards old age or suffering, and changing one's perspective to cure aversion towards skillful things like seclusion, are all examples of changing one's perspective or view of a situation, to turn unwholesome into wholesome.