It seems like torture should work.
When someone won't talk, torture makes the cost of not talking high. Incentives make them talk.
But what if they lie?
Make the credible promise that more torture will happen if their information doesn't turn out, or contradicts what you already know. Incentives make them tell the truth.
Is torture not incentive enough?
Turn the torture up a notch. Now they have more incentive to talk / tell the truth.
So it seems like torture should work based on deductions from normal assumptions we have about human beings and how they respond to incentives. This is the plain reason torture works.
So why do a lot of people deny that torture works?
One possible reasons is historical data. We have tortured. Did it work? I'm sure there's data out there and maybe it turns out the other way. Data on these kinds of issues tends to be messy anyway, so it ought to take a lot of clear data to undermine the plain reason torture works.
Most people; however, are not informed on the data. So I suspect most people think torture doesn't work because they think torture is unjust. There is a suspiciously high correlation between the belief about whether torture works and whether it would be unjust even if it doesn't work, even though the neither answer informs on what the other answer should be.
People often rationalize for why what is deontologically moral also happens leads to good results. It's like anything they believe to be morally right cannot have any costs whatsoever.
A reasonable person might say, torture works, but we shouldn't do it unless it's really important because torture is just a really bad thing to do to someone, even an enemy. I think that's how we would normally navigate the moral domain in our own lives, and so that's the guide public policy should probably follow.