This gets the direction of cause and effect backward. The argument is that how one responds to problems ultimately affects the occurrence of a specific condition (gum disease). (A) instead suggests that the occurence of a painful condition affects how one responds to problems. Because (A) supports a completely different explanation from the author’s own conclusion, this can’t be a necessary assumption.

The author draws a causal connection from stress to immune suppression to gum disease. But the premises give no reason to think that people with gum disease have experienced stress. Instead, gum disease is associated with refusing to think about problems. The author must assume that refusing to think about problems causes stress, which triggers the causal chain leading to gum disease.

This means that people with high stress levels—and therefore suppressed immune systems—are the kind of people who are less likely to have gum disease. This weakens the argument that immune suppression contributes to gum disease, so it can’t be a necessary assumption.

This suggests an alternative explanation for why these people are less likely to have gum disease: it’s not about stress levels or immune suppression, but rather that these people are proactive about seeking dental care. Since this is unrelated to the explanation the author argues for, it can’t be a necessary assumption.

This weakens the argument. People who refuse to think about problems are the ones more likely to get gum disease. If refusing to think about problems might help avoid stress, then we have less reason to point to stress (and the resulting immune suppression) as a contributor to gum disease.