It is about looking at mortality as some kind of disease and not a common thing that happens to all living beings.
As a human, I am afraid of death as the most of us. I like to toy with the idea living forever, or at least hundreds of years...
But looking at our society now. As the average lifespan getting higher, more people stay in jobs longer as usual. The young wont have any jobs, because their parent will stay in the positions. In the end the old would have to sustain the young and soon after that, no one would want to have a child, because who needs another hungry mouth.
Of course as the 1st world country citizens will afford living a longer life, 2nd and 3rd ones wont. This will create a massive gap between nations. Like we didn't have that already.
And we don't know how the human mind could handle this anyway. Maybe you would go actually mad after 200 years of living.
And as I said. The extra years always add up to the end. Maybe you live 200 years, but 2/3 of that is spent being old and useless.
As highly appreciated and acknowledged people warn us about the ramifications of A.I., so we should be extremely cautious about banning death.
To be honest I would be less afraid of A.I. as the consequences of immortality.