The opposite of hypochondriac is denial of having a medical illness. There is no single word that is the opposite hypochondriac, which is a person who believes that they have a serious medical illness, despite their doctor and medical tests stating that they are healthy.
Men in particular have a problem with denial of having a medical illness. Among groups of men, they see having an illness as weakness, and therefore men will ignore their symptoms and underlying illness so as to not be scrutinized.
Western culture as a whole, where it is highly competitive, looks unfavorably on someone who has an illness. Therefore, people will tend be in denial of having a medical illness due to our hypercompetitive culture.
