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fubarobfusco comments on If there was one element of statistical literacy that you could magically implant in every head, what would it be? - Less Wrong
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Noise happens. Even if X is predictive of Y, it's rarely perfectly predictive.
For instance, suppose that 1000 students take a math test, then take a different math test that covers the same material with different problems. It is highly likely that their rankings on the two tests will be strongly correlated. It is highly unlikely that their rankings on the two tests will be exactly the same.
And it is quite possible that a few students will do vastly better on one test than the other, due to things that have nothing particularly to do with their mathematical ability. If you give a math test to a sufficiently large student population, then some student's boyfriend will have gotten hit by a car on the morning of the math test. That will probably mess with their scores.