Is living forever or having a greatly extended lifespan desirable?

"One person with whom I was arguing about this acknowledged that eliminating disease would be a good thing, but insisted that physical and mental aging should be preserved"

Perhaps you could ask them what their most loved activities are, and then point out to them old people who are less able to enjoy those activities because of their decrepit body and/or mind. Then point out that the whole reason we want to cure a disease is that we don't like being decrepit, meaning that for all intents and purposes aging is a disease.

I think part of the resistance to the idea of halting aging is based on people not wanting to be upset about what they believe to be inevitable. By arguing that aging is actually desirable, people can convince themselves not to be so upset about their body falling apart. I see their reasoning as a riff on retrospective rationalization (I'm not sure what cognitive bias that is), but it's arguably to some extent a psychologically healthy bias. Most of us have considered the process of getting old, and have integrated that somewhat somber consideration into our world view. But really, we don't want to walk around with long faces, so many of us stubbornly refuse to have a negative attitude towards it. In fact, we want a positive attitude towards aging, and that really requires believing in a narrative about how getting old is natural, healthy, and desirable. In a splendid act of double-think and compartmentalization, we somehow overlook the contradiction that becoming old means becoming decrepit, and that becoming decrepit is now somehow healthy and desirable. And of course we conveniently allow ourselves to slip back into the comforting fallacy that "if it's natural then it's good".