This idea baffles me. Do people really think you can't steal some food in a pinch to save a starving person's life? Or kill one innocent to save a thousand?
I think the only reason anyone believes this besides being raised to is because of contrived examples that scare them. Often these examples are red herrings (they're situations where consequentialism doesn't entail what the presenter says it does), but others are more honest. I'll give the strongest example I can think of by far:
A scenario I first read on philosophyexperiments.com titled "The Backpacker" (I've seen it discussed in a few other places since then). To preserve all details of the original statement, I'll copy-paste it here:
Dr Georgina Mouse is a truly great surgeon, so great that any organs she transplants always take. At the moment she has five patients who need organs (lungs, kidneys and a heart). If they do not get those organs today, they will all die; if organs are found for them today, Dr Mouse can transplant the organs and they will all live. The time is almost up when a report comes in that a young backpacker has come into the hospital for a routine checkup. It turns out he is in excellent health, and has exactly the right blood type to guarantee success if she transplants his organs into the patients. All she needs do is cut him up and distribute his parts among the five who need them. Assuming the backpacker doesn't consent to giving up his life to save five other people, is it morally permissible for Dr Mouse to take matters into her own hands, and operate anyway?
Most people - myself included, when I first read this - have an incredibly strong intuition that the answer is no. First, I need to clarify something about my position.
There's a difference between the ends justifying the means and purifying them. Even if Dr Mouse is right to murder the backpacker, it is still murder, and if they were to meet in another world, she would owe him her life in restitution. The ends justify the murder, but they don't make it not a murder.
But I doubt that makes most people much more satisfied. So to bridge the enormous discrepancy between intuition and consequentialist logic, I'll make an argument from both directions. First I'll explain why Protagonist consequentialism doesn't see this as a 5 to 1 - it's a lot closer than it looks (but I do stand by killing him).
Factor #1: there is a difference between killing and letting die; it's the value of consent. A way of looking at it is that (see how consent and compassion are two separate values that stack) you're not destroying one person's life and saving another's (which would indeed balance out as x Compassion + x Cruelty), but destroying one person's life and violating one person's right to their life to save one other person. (The people who were already dying do not have a "right to life", because that's not how rights work.) So it takes more than a 1 to 1 ratio to justify this, even before the other considerations.
Factor #2: redistribution of fortune is a prime wrong (the value of Fairness), and this is true even if it's consensual. To be fair, this is probably a pretty rare belief, but I find that considering it as one makes the implications of my moral system align far closer to my intuition.
Factor #3: the difference in the quality of life they're likely to have if they live. The five patients are dying and it's as best not established that an organ transplant will restore them to full health and a normal life. The backpacker, on the other hand, is explicitly stated to be in excellent health. So you're destroying one probably enjoyable life to maintain five lives that are likely to be far less enjoyable for the people living them. (This factor should be disregarded if the scenario assumes that the patients will return to full health. I've heard it stated that way somewhere else, but this statement didn't say that, so I'm pointing out that it makes a difference.)
Factor #4: the backpacker is having this ultimatum laid on him out of nowhere, so he gets no closure if he ends his life here. Even if we believe it's right to murder him here, we must recognize that it's crueler than murdering someone with a few days' warning. Albeit, this is probably a small factor in the scheme of things.
Factor #-1, which works against my argment: the patients have presumably already suffered greatly at the hands of their illnesses, and so, by the Prioritization principle, compassion to them has more weight than compassion to the backpacker. These two probably mostly cancel out; but I saw fit to mention both to prevent your intuition from being biased by noticing only of them. (I noticed Factor #4 when I first wrote this article and only noticed the opposite effect while editing it years later.)
Another thing I want to say while I'm at it: try considering this from any perspective other than Dr Mouse's. Imagine if one of the patients had the choice. Would you find it equally obvious that the dying patient would be wrong to kill one person to save themselves and four other innocents? Or even the backpacker's perspective: wouldn't you agree that he's incredibly selfish to refuse (even if it's understandable)?
I'll have to admit here that according to my value system, refusing to make this sacrifice makes him a worse person and thus makes his life worth somewhat less. This works against the argument I'm trying to make here.
But actually, due to the self-anchored perspective effect I mentioned in my article on the moral conflict, the backpacker may truly be justified in refusing to sacrifice his one life to save five strangers. He might consider himself important. And he might be right. Maybe he's involved in something that critically affects more than five people. But he doesn't know anything about these patients. For all he (or we) know, they're as likely to be bad people as they are to be good. But even if he's justified in refusing, that doesn't mean Dr Mouse shouldn't kill him - see the moral conflict article.
But this probably still isn't enough. I realize there still seems to be a tremendous discrepancy between your intuition and what seems to be inevitable if the end justifies the means. So for the rest, I'm going to point out a significant amount of bias in the way the problem is stated.
The first hint of bias is that the 5 people are introduced as one entity. Every time they're referred to, it's as "the five" and not as individuals.
It's also worth mentioning that we don't know anything about any of the dying patients as people. They're just "patients" and that's all we know about them. Video game story writers and critics will be intimately familiar with this effect: we find it hard to value the lives of those we don't know anything about and thus can't easily feel for. But we know something about the backpacker as a person: he's a backpacker. It's not much, but it exists. He has also taken an action in the story (he came to the hospital for a routine checkup), which probably furthers this effect. Finally, he has an assigned gender, even if it's arguably the less advantageous one, which goes a long way toward humanizing him and biasing our emotions toward siding with him. We've been given a basis to imagine the backpacker's perspective, but the scenario hasn't done anything to help us imagine the patients' perspectives - it's done the opposite by collectivizing them.
Then there's the unnecessarily vivid way the murder is described. "Cut him up" is very gory language that suggests an image of Dr Mouse assaulting the backpacker with a knife and spilling his blood everywhere while he screams. To increase the relevance of the example to the principles at stake, we should assume that Dr Mouse has a way of killing him quickly and painlessly (since the suffering of the five patients isn't mentioned at all either).
Phew, that was a lot. I hope now you can see how it's not hard to accept that the answer to the question is "Yes".