One reason for thinking that consequentialism must be correct is that otherwise it might be morally wrong to make the world a better place, and that's just absurd. To bring out the force of this argument, consider the old 'Organ Harvest' scenario, where a doctor could kill an innocent passerby so as to transplant his organs into five needy patients (one who needs a heart, two needing kidneys, etc.), and thereby save their lives. Intuitively, we think it must be wrong for the doctor to kill, no matter the beneficial consequences. But can this intuition survive rational reflection?
Let's remove homicide from the picture, and consider two alternative possible worlds. In the first world, the five patients die, and the passerby goes on to live a happy life. In the second world, the passerby's head falls off (by brute natural chance) just as he's walking past the doctor's office. The doctor then uses the man's organs to save the five patients, who each go on to live happy lives. Further suppose that all else is equal - there are no other relevant differences between the two possible worlds. Which world is better? Surely, based on the descriptions provided, we must judge that world #2 is the better one.
Now suppose that God lets you choose which of the two worlds to actualize. (After making your decision, the divine encounter will be wiped from your memory.) You get two buttons. If you press the first button, the real world will be world #1, and the passerby will live. If you press the second button, the real world will be world #2, and the five patients will live instead. Which button should you press? Again, it seems obvious that you should press button #2. Given the option, we should choose to make the world a better place rather than a worse one.
Let's elaborate on how it is that the passerby's head happens to fall off (in the second world). It turns out an invisibly thin razor-sharp wire had been blown by a freak wind which fixed its position at neck height where the man was walking past. (No-one else was hurt and the wire soon untangled itself and blew away harmlessly into the nearest dumpster.) This presumably will not alter the moral status of any of our above judgments.
Now suppose that, instead of two buttons, God gives you a length of razor-sharp wire with which you can make your decision. By putting it straight in the dumpster, you will realize world #1. By fixing it in the appropriate place, you will realize world #2. Again, God will later wipe all memory of your decision and actions. What should you do? The situation seems morally equivalent to the previous one. There don't seem any relevant grounds for changing your choice. Thus the right thing to do, in this bizarrely contrived scenario, is kill the passerby.
So why shouldn't doctors go around killing people? Why, it would have bad consequences, of course! In the real world we are never perfectly rational and fully informed, so we can easily make mistakes when attempting utility calculations. There's the risk that you would be found out, which could result in widespread panic and a "climate of fear" that would make life very unpleasant for everyone in the society. Moreover, the action itself would probably warp your psychology, and without God to reset your brain, it might dispose you to commit wrong (utility-thwarting) acts in future.
So the utilitarian can agree that homicidal doctors are almost always acting wrongly. But in any (bizarrely unrealistic) scenario where it would actually do more good than harm, we must judge that it would indeed be right. (Given that such situations would never arise in real life, this judgment has no practical import.) Though this initially seems counter-intuitive, further reflection can support the judgment. The real absurdity is not the utilitarian conclusion, but the bizarre scenario that critics of utilitarianism are appealing to here.