If it is difficult to determine which foods cause migraines, then some foods that cause allergic reactions might not have been demonstrated to do so. Hence, if choice A is true, eliminating foods that have been demonstrated to cause migraines might not eliminate migraines, even if food allergies are the only cause of migraines. Choice A is the best answer.

Neither the fact that some food allergies do not result in migraines (choice B), nor the fact that few allergies result in symptoms more severe than migraines (choice E), explains why restricting one’s diet does not stop migraines. Choice C suggests that migraine sufferers do not naturally avoid the foods at issue. Choice D reiterates the information that eliminating certain foods does not usually solve the problem.
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Although migraine headaches are believed to be caused by food allergies, putting patients on diets that eliminate those foods to which the patients have been demonstrated to have allergic migraine reactions frequently does not stop headaches. Obviously, some other cause of migraine headaches besides food allergies must exist.

Which of the following, if true, would most weaken the conclusion above?

A.Many common foods elicit an allergic response only after several days, making it very difficult to observe links between specific foods patients eat and headaches they develop.

B.Food allergies affect many people who never develop the symptom of migraine headaches

C.Many patients report that the foods that cause them migraine headaches are among the foods that they most enjoy eating.

D.Very few patients have allergic migraine reactions as children and then live migraine-free adult lives once they have eliminated from their diets foods to which they have been demonstrated to be allergic.

E.Very rarely do food allergies cause patients to suffer a symptom more severe than that of migraine headaches.

Can anyone explain me why 'C' is incorrect? I do find the same topic that had been discussed few years back, but couldn't explore why 'C' is incorrect as the contest was b/w A and D. I got to know why A is correct, but couldn't get the reasoning for why we should make it C as wrong.

Only (A) weakens the conclusion.It could be that people can easily overlook the actual culprit foods that cause the migraine headache

If it is difficult to determine which foods cause migraines, then some foods that cause allergic reactions might not have been demonstrated to do so. Hence, if choice A is true, eliminating foods that have been demonstrated to cause migraines might not eliminate migraines, even if food allergies are the only cause of migraines. Choice A is the best answer.
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.It could be that people can easily overlook the actual culprit foods that cause the migraine headache . Hence A

now, I understand that studying the wrong options means studying how the pattern can be right + the common trap in gmat.

The key issue is most of the wrong options are stupid and have little values -> only the right answer is what test takers must learn.
Nevertheless, wrong options in one question can be the right answer in another question, or the wrong options contain a common trap.

Anyway, A is a very common and important pattern in gmat.