It's the 'indefinite' part that I react negatively to. I don't have a good impression of people who are obsessed with abolishing death, as opposed to your example of maximizing quality of life (or minimizing illness) without getting too hung up on overall age.
Actually they said: "Aging isn’t a law of nature." But it kind of is. Almost all biological organisms age and the ones that don't are much simpler than us. That's not to mention entropy which is both a law of physics and dictates an inescapable form of aging for the universe as a whole.
They also said there isn't a physical reason, that is often meant to mean "it isn't a law of physics".
The fact that something happens doesn't mean it's a law of anything. Cars didn't exist before we built them - no law of "no cars". People died of TB before we had a cure - no law of "TB". Same for various types of cancer.
In practice when someone says "live forever", they don't mean to imply they'll live the 10^100 (or whatever the guestimates are) years to the end of the universe. They mean they'll stop aging in the sense that we do now. Maybe we could live to 10,000 or 50,000 or whatever. You can always get hit by a bus, or get some strange disease from a bat, or whatever.
