I'm glad you asked about this - let me see if I can make it clearer
"The compassion of the wise man does not render him a victim of suffering. His thoughts, words and deeds are full of pity.
But his heart does not waver; unchanged it remains, serene and calm. How else should he be able to help?"
This means the wise man doesn't become a victim of his compassion ... being a victim of compassion seems to be what @ufology is concerned about ... as expressed in the desire to be dispassionate or to feel less compassion in exchange for the ability to do something about a situation ...
... a very common example is something I heard frequently when I was a foster for the Humane Society. People would say
"I'd love to be a foster for the Humane Society but I'm so compassionate, I wouldn't be able to give them up to their new owners, it would tear my heart out ... therefore I'm not going to be a foster."
or
"I'm not going to the animal shelter to find a pet, because I'd want to take them all home ..." (as a result of this - the animal they might have selected could end up euthanized) - so the person in both cases couldn't tolerate the emotional pain they felt compassion would bring to them, so they didn't act at all.
People often say this about relatives in the nursing home - that it's just too painful to visit.
So, in Buddhism, the opposite choice is made - to face the most painful of situations skillfully.
What the passage above says is that wise man's thoughts, words and deeds are full of pity (compassion is a better word - "pity" here is not a good translation) ... but his heart does not waver in other words, he doesn't let the fact that he is full of compassion prevent him from acting ...
his heart remains unchanged means that it is serene and calm (and it means that he is resolved to act for the good) ... the last part how else should he be able to help? means if he didn't maintain serenity and calm, he wouldn't be able to act effectively - he would be like the people who didn't become animal fosters because they felt it would be too painful, he would turn away.
So, this is actually the opposite of
Can we really manage not feeling the suffering of others? What gives us the right to? And how does one manage that? I sometimes feel that much of Buddhism amounts to an effort to escape from the human condition, an effort to become alienated from natural consciousness and its tribulations. To be as far out of the world as one can be while remaining in it
... in that the passage says that you move forward with a heart full of compassion, maintaining serenity and calm in order to act effectively. This is not at all unlike the kind of training given to emergency workers - this was hammered home to us in EMT class ... if you get to the scene of a car wreck and you fall apart - you are worse than no good, you are a danger ... so you act according to your training and you get the job done then you go home and deal with all the emotion. The problem was we weren't given any tools to deal with it.
In Buddhism you do that training in meditation, which is not the popular vision of escaping to blissful states, but rather you stabilize the mind and then grapple with the passions, at times even evoking painful situations in order to deal with them. It really is like emergency or martial arts training. Since I've benn meditating, I've felt a greater range of emotions and more intensely.
Pema Chodron I think is one to make this clear in Western language. The problem with quoting from the suttas as above is that everything is interlinked and words are used in specific ways ... but sometimes I like to take the chance that it will convey.
Here are some quotes from Pema Chodron that might have better served my point
Pema Chödrön Quotes (Author of When Things Fall Apart)
“…feelings like disappointment, embarrassment, irritation, resentment, anger, jealousy, and fear, instead of being bad news, are actually very clear moments that teach us where it is that we’re holding back. They teach us to perk up and lean in when we feel we’d rather collapse and back away. They’re like messengers that show us, with terrifying clarity, exactly where we’re stuck. This very moment is the perfect teacher, and, lucky for us, it’s with us wherever we are.”
“Compassion is not a relationship between the healer and the wounded. It's a relationship between equals. Only when we know our own darkness well can we be present with the darkness of others. Compassion becomes real when we recognize our shared humanity.”
That's all well and good, Steve, but I don't think one needs to become a Buddhist or meditate in order to figure it out. It's the way most mature people learn to manage their discomfort for the benefit of others. 'Sitting on one's own pain' is, I believe, one of the recommendations shared in Alcoholics Anonymous.