Summary: At a steady state of population, extended lifespan means taking resources away from other potential people. Technology for extended life may not be ethical in this case. Because we are not in steady state, this does not argue against working on life extension technology today.
I make a slightly different anti-immortality case here:
https://harsimony.wordpress.com/2020/11/27/is-immortality-ethical/
Summary: At a steady state of population, extended lifespan means taking resources away from other potential people. Technology for extended life may not be ethical in this case. Because we are not in steady state, this does not argue against working on life extension technology today.