The doctor doesn't ignore medical opinions that cut against her conclusion. She acknowledges in her very first sentence that being overweight has been linked with health problems. Also, it's not inherently flawed to reach conclusions that go against other people's opinions. So even if you interpret "ignore" as "go against," (which isn't what "ignore" means), (A) would still be wrong.

The doctor never defines "healthy," but she doesn't need to. We're allowed to make arguments without providing definitions of the words we use. We can expect people to understand the words based on standard dictionary definitions and context. So failing to define "healthy" isn't why this argument is unpersuasive.

This points out that the doctor doesn't account for individual variation in appropriate weight. But the doctor doesn't assume that everyone has a similar appropriate weight. The premise is about a general relationship between the slightly overweight and the considerably underweight. What is "overweight" and "underweight" can vary from person to person, but the general relation between the two groups still holds.

Where is the "property that would suffice to make the person unhealthy"? And where does the doctor state that slightly overweight people don't have that property? These descriptions don't map onto anything in the argument.

For (D) to be correct, the argument would have had to say something like, "X guarantees you're unhealthy. But people who are slightly overweight don't have X. Therefore, being slightly overweight is enough to make you healthy." That would be concluding that because someone lacks a property that makes people unhealthy, they must be healthy. But the doctor's argument doesn't do that. Instead, she identifies a relative property (being healthier than considerably underweight people) and treats it as proof of an absolute property (being healthy).