"Counter-intuitive" is one of the current jargon words, and very useful it is, too.  It means something that goes surprisingly against what your commonsense or "intuition" might expect.

One example is this: There are studies going on to determine what other factors might be causing the overweight/obesity problem of our society, because the extent of the problem can't be fully explained by the twin causes of over-eating and under-exercising.  One factor that seems to be emerging is that we are not getting enough sleep.  Whereas in in 1960 we averaged 8 1/2 hours per night, these days we average less than 7.  And a number of studies point to a correlation between lack of sleep and overweight - not, as you might suppose, because the person sits up late and snacks, but in a controlled study where the same amount of food was eaten, the less sleep resulted in greater weight gain.  Now, this is quite "counter-intuitive" because you would expect that staying up late, or sleeping less, would be burning more calories than lying in bed asleep. (Article "Supersize Surprise" in New Scientist 4 Nov 2006 - can't find online link to the article, think you have to subscribe).

Don has what we used to call bed sores but they now call pressure sores, and the treatment is - yes, counter-intuitively - keeping him in bed and not letting him get up until they are quite healed. The explanation is that you don't get these sores simply by being in bed, if your care is being managed properly, and so they are not bed sores.  You get them by having too much pressure on the one spot. Don had a short spell in hospital and came back with pressure sores. He is not able to turn himself over in bed, so the staff have been very diligent for the past three weeks, keeping him on a special air mattress, and turning him every two hours.  And not letting him get up and and be sitting up with further pressure on his spine, exacerbating the problem.

Hey presto!  Counter-intuitive it might be, but it works, he is pretty much healed, and he is now getting out of bed every second day, with the possibility of resuming home visits in the near future.