That overpopulation exists at all is one of the most prevalent delusions in the modern world: thanks to the environmentalist movement, a cause that has ascended near to the status of civic religion, the average fellow in the street thinks that there are too many people alive today, that resources are stretched to breaking point, that the future is one of Malthusian decline, and that horrible poverty in the third world is caused by the existence of too many people. All of these points are flat-out wrong. Humanity is wealthier and has greater access to resources today than at any time in history, the variety and amounts of available resources are growing at an accelerating pace due to technological progress, the earth could support many times more people than are alive today, and where there is poverty it exists due to terrible, predatory governance and the inhumanity of man - it exists due to waste and aggression amidst the potential for plenty.
Even this pro-longevity piece subscribes, as many do, to the false idea that somehow we are consuming too many resources and will run out. This is silly: resources are infinite, because through technological progress we constantly develop new ones. People live in an age of change, with each new decade clearly different from the last, and yet live under the assumption that everything will remain the same going forward. Being worried about running out of anything that we use today is like being worried about running out of candle wax in 1810, or running out of room for horse breeding operations in 1840, or running out of food in 1940. All false concerns, and all false for exactly the same reasons: we are not static consumers of resources, we are net producers of resources.
Make no mistake, it'll take us a long, long time to get there, but we'll eventually find a way to halt the aging process. Owing to advanced medical, regenerative, and cybernetic technologies, future humans will enter into a state of "negligible senescence," a condition marked by the cessation of aging and the onset of everlasting youth. It sounds utopian, but as biogerontologist Aubrey de Grey has repeatedly noted, it's simply an engineering problem - one that's not intractable.
I've been debating this issue for the better part of a decade, and I've heard virtually every argument there is to be said both in favor of and in condemnation of the possibility. I'm not going to go over all of them here. But without a doubt the single most prominent argument set against radical life extension is the issue of overpopulation and environmental sustainability.
As a final note, there's a certain inevitability to radical life extension. It's the logical conclusion to the medical sciences. So rather than futilely argue against it, we should come up with constructive solutions to ensure that it unfolds in the most non-disruptive way possible.