holding up an outlier to refute a true, factual statement

A friend of mine is a Christian Scientist. She believes that illnesses exist only in the mind and can be cured by "right thinking" and prayer. She is 72 years old. Recently she complained to me that a lot of her friends have been dying lately, and she asked me why I thought that was. I said it's because both she and her friends are in that age cohort during which people start to die of diseases with greater and greater frequency. In other words, she and they (and I, by the way) are OLD. She hated this answer because she doesn't like to acknowledge that time may be running out for her. So her response to my comment was an indignant "young people die too!" Of course they do. Babies too. Fetuses can die in utero. Everything that lives eventually dies. Even the sun will die. That doesn't change the fact that more and more of her friends are getting sick and dying because they are old. This is not a weird coincidence caused by Satan or an evil wind; it's a consequence of aging.

I've discovered that this tactic for refuting a true statement is fairly common. People will sometimes go to absurd lengths to avoid acknowledging that sometimes generalizations are true, because they are not just generalizations, they are descriptions of fact. What is the fallacy at work here?

Classic non-sequitur and possible (implied) strawman . She offered a refutation to an argument that you did not make. Had you made the argument "only old people die" her refutation would be appropriate. But you didn't.

She hated this answer because she doesn't like to acknowledge that time may be running out for her.

I never fully understood this. True believers in enteral bliss with Jesus should be psyched to die and end this pathetic, sinful, human existence. But that is a whole other conversation :)

It’s not a fallacy. It’s a psychological disability defined as
Anosognosia is a deficit of self-awareness, a condition in which a person with a disability is unaware of its existence. It was first named by the neurologist Joseph Babinski in 1914.