You need to build a driveway up to your new house, and there are two possible routes, each one with a single maple tree in the way. One of the trees is very old, but quite healthy, standing at least 50 feet high. The other was just planted a few months ago, so is still quite small.
You're not the one that's going to cut the trees down, and the cost to do so will be the same in both cases (let's say that the higher cost to cut down the bigger tree is offset by the fact that the person cutting it down wants the wood for himself) - which tree do you cut down, and why?
Now, this doesn't seem like a moral issue. Almost everyone would cut down the smaller tree, for several reasons: it would take less time to grow a new one of the same size, we wouldn't be destroying as much previous "work", etc. Very logical, can't really argue with it.
But I lied. When I said "maple tree", what I really meant was "human", and when I said "you need to build a path to your house," what I really meant was "we're all in a flimsy lifeboat, there's a nasty shark circling, and it wants it some tasty human gubbins[1], so we either need to toss overboard the 50 year old award winning medical research doctor with a loving family of six waiting for him at home, or a newborn baby. Or else we all die!"
[Edit: As I pointed out in response to some of the comments, I probably should have made the doctor younger, to avoid questions about whether he's already used up most of his potential. I'd encourage you to think about what age he'd need to be to change your decision...]
Anyone here actually willing to stand up and say they'd toss the baby? Because from a pure utilitarian point of view, it's the logical thing to do - a newborn baby is a roll of the dice, likely to turn out as a completely average adult, with zero expected value above and beyond any other newborn baby that the same couple has, so they might as well just make another one. OTOH the professor has proven himself to be near the top of the usefulness curve, and the expected value of his remaining years is likely far greater than that of the newborn, even after we factor in the mother's grief over losing her baby.
It's a rare person that would actually make the choice to toss the baby - I certainly don't think I could, but I can't really pin down my logic to anything more compelling (in a rational sense) than "But it's a baby, for God's sake, it just feels so wrong!"
[1]: A strained extension of the term "gubbins" (http://www.thefreedictionary.com/gubbins) outside its usual meaning? Perhaps. But screw it, "gubbins" just sound like they would be so damned tasty, I stand firmly behind my use of the word.