There’s a species of sea turtle which doesn’t age past maturity. They grow up, and then they’re just the same forever. They never die of old age.
Why, you may wonder, are we not all up to our necks in immortal sea turtles? Because they still have predators, diseases and accidents.
If science solves the problem of human ageing, people will still die. Even if science cures all diseases, people will still die. It may help us live longer, but each of us gets our turn. Every turtle, and every human.