Like the idea here is either a singular human or a member of a group of Humans in Equestria seeing a pony character in great distress and pain and rather than using the power of Friendship. uses the power of the almighty bullet to put them out of their misery instead. Silently cocking his pistol and quietly aiming at the back of said pony's head. However the other pony characters, mostly the friends and family of this suffering pony catches said human character in the act, just when they're ready to pull the trigger.

How do expect them to react to someone attempting to relieve a member of their kin of pain by blowing their brains out instead of consoling them?

like imagine an alternate "Rockhoof and a Hard Place" where a human character is presents and is caught doing the above to Rockhoof? Him not knowing since he'd been blindfolded.

They'd see it as an attempt at murdering their friend/family member, the human would be a psychopathic villain in the eyes of the ponies

7959743
Considering that in humans, euthanasia is a crime against humanity that can get you life in a UN prison, I would figure that the ponies would probably feel the same.

However there would be caveats depending on the situation, like if the human and pony took a nasty spill down a gorge together. The human is reasonably okay, no immediately life threatening injuries like internal bleeding or a massive gash that severed an artery and in now fountaining blood. The pony is much worse off, basically ten different kinds of messed up, massive cranial injury, punctured lung, serious internal bleeding and in immense pain. If help is more than a day out, quickly ending one's suffering if they explicitly asked for it, then the ponies may not feel so repulsed by the act, especially if the alternative is long term suffering before dying miserably.

I believe you meant mercy killing as opposed to euthanasia.

Throughout human history sometimes mercy killings were necessary. Like a soldier turning the gun on one of their comrades who was trapped in burning wreckage and no one could get them out. Stranded survivors having to live on dwindling resources while waiting hopefully for a rescue and one of their number falls deathly ill, it might be necessary to kill the deathly ill person to prevent the disease from spreading to others in the party. A country suffering through a famine, the sick, the infirm, the greedy and the elderly might be killed or abandoned in the wilderness to help preserve what little food is left. Mercy killings are never taken lightly as you're killing one of your comrades or in-group. Euthanasia generally involved dehumanizing a class or group of people so you don't feel bad when they're killed, it a PC way of saying genocide and/or ethnic cleansing.

7959748
And what would you call it when someone suffering from a terminal illness goes to a professional so as to get their lives ended on a particular date, like in Canada or Switzerland?

7959745
but what if the pony was asking, no, begging for death?

7959748
what about for Rockhoof's case, would it be "right" to mercy kill him?

7959781
I don't think that matters in the eyes of the ponies

7959779
Assisted suicide. The doctor hooks you up to the machine or gives you the vial of drugs that will stop your heart and lungs, but you have to be the one who pushes the button or drinks the vial. In the event that your disease has progressed to the point where you lose the ability to act on your own(such as Alzheimer's, advanced Parkinson's, etc...), if you have the proper documentation that states in the event you are unable to act on your own behalf because the disease had advanced to the point it has robbed you of your physical and/or mental faculties, then your spouse or your children or another loved one or your lawyer will be the one to press the button or pour the vial down your throat. None of the doctors or nurses can be the one to carry it out, only hook you up to the machine or supply you with the vial.

With assisted suicide, you're given every opportunity say that you don't want to go through with it, up until you press the button or drink the vial. I support assisted suicide because you're giving someone who is in the final stages of a terminal illness the opportunity to go out on their own terms, instead of languishing away in a hospital bed for months or even years. I also support hospice care. Everyone deserves to go out on their own terms, whether that's being surrounded by your loved ones while you fade from this world or going out fast with drugs that stop your heart and lungs, sparing yourself and your loved ones months or even years of pain and heartache, and it even helps with the grieving process knowing they went out on their own terms.

A couple of years ago Canada passed a disturbing addendum to their assisted suicide laws which allows to government to step in and implement it, even if they and/or their loved ones does not consent. Though I have yet to hear anything about the Canadian government forcibly giving anyone the lethal drugs, the Canadian parliament has yet to strike that addendum. That means that there is the potential for whatever party currently sits in the majority, they could exterminate anyone they deem as undesirable and it would be perfectly legal under the law.

7959782
That would entirely depend on context and circumstances.

If they're suicidal, that means they could unwilling to do it themselves because of personal and/or religious reasons, and if you one to the dome, that would be murder.

If they're in the middle of a town, that again depends on the circumstances. If they're trapped in burning wreckage, no one can get to them because the flames are too hot and they would burn to death before the flames could be extinguished, then putting one to the dome would be a mercy killing. If they're lying on the ground severely injured and help is at most 20 minutes out, and you dome'em, that would be murder.

If you're stranded in the wilderness together and they have serious, but not life threatening injuries, doming them would be murder. However if you are both about to be attacked by a pack of starving wolves or coyotes or timberwolves or a manticore, and they say, "Kill me. I'm injured and will hamper your ability to fight. They/it will go after the easier meal and you can get away.", that's a much more legally, ethically and morally gray area. If you're both stranded in the wilderness and they have severe, life threatening injuries, and help is at best several days out, and they might survive the day, but they won't survive the night, doming them at their request would save them the suffering, just make sure to clearly mark where you bury them so their remains can be exhumed and placed in a proper grave/mausoleum/crypt/tomb.

In your initial post, you were referencing the episode where Rockhoof was having trouble adjusting to the modern world. He was feeling useless and depressed and suicidal. He needed psychiatric help, not petrification or taking one to the dome piece. Don't try to pull an 'Aha, gotcha!' move on me, I get it enough from the white, conservative, Evangelical Christians here, who are also Confederate fetishists and love playing the whataboutism card.

7959748
Yep

It’s a difficult topic, but a coup de grace on the battlefield is a far cry from medical euthanasia.

ME is a gray area but also one that upholds the beneficence clause of the Hippocratic oath. Let’s say our patient is suffering an incurable cancer that is eating away at their bodily organs. No amount of pain killers will dull their agony and there is no hope for recovery. The patient, still coherent and aware, says that they want to die peacefully within the company of their loved ones before the cancer sends them into a state of delirium. Would it be ethical to ignore the patient’s last wish? I don’t think so, but it is a heavily debated issue for good reason.

I think ponies, though generally more progressive minded than humans, would still suffer disagreement over this issue. Although ME is politicized in our world, the ethical conundrum exists deeper than concepts of personal politics. A pony lived in a culture where life and happiness are utmost. To deny the patient’s wish would be to subject them to a terrible fate. To accept the wish would mean that they are bringing someone’s life to an end through direct action.

It’s certainly a tough nut to crack.

As for a mercy killing… it’s blood on the sand. The dripping maw of the battlefield is forever hungry and petty matters of ethics are no more than a bone be tossed to the side after each strip of meat has been torn away. Gnashing teeth and growling stomach. Only after the meal has been digested will the warrior suffer the realization of what they have done.