No one said to kill off all of humanity. Certainly 'bad' people have died in the long (short) history of humanity without the remainder of the species disappearing.
Life doesn't occur without death. Death is a necessary component. Life _comes from_ death.
Walk into an old growth forest some time.
You said: "It’s extremely important that we [die] — if not just for getting rid of some of humanity’s worst humans"
Their retort is that this is a very blunt instrument. You are advocating killing literally billions of humans (not all at once), just to make sure you get the bad ones. That's a hell of a lot of collateral damage.
I'm ambivalent on the question of improving healthspan and longevity, but I agree with the other person that this is a bad argument against it.
I think you misinterpreted my comment. I was not advocating for killing. Killing is an unnatural process.