There's a difference between increasing the lifespans of people and increasing the numbers. The difference between someone living forever and someone living 20 years can be made up for by having an extra kid every 20 years. The bottleneck is how many people the world can support, not how many are born.

Also, saving the lives of everyone on Earth implies allowing them to have kids, and their kids to have kids. It's saving the total number of people the Earth will support, not just the ones alive at the moment.