Many varied arguments are made against attempts to extend human life spans through medical science: overpopulation, economic impacts, boredom, stasis, that people would be aged and decrepit for longer, and so forth. The only thing they have in common is that they are all fairly ramshackle, and tend to fall apart in the face of even a mildly rigorous look at the data and the evidence. Not that this state of affairs seems to have converted all that many people to our side of the tracks. Arguments against living longer in good health have more to do with emotion, comfort zones, and signaling to peers than anything else, I'd say. The same people who, when prompted, declare that everyone should age to death on the same schedule that exists today also visit doctors when sick, would rather not live with the life expectancy of a few hundred years past, and are generally supportive of efforts to defeat age-related diseases such as cancer, Alzheimer's disease, heart disease, and so forth. They are very inconsistent in word and deed.
I see opposition to life extension as just one of many manifestations of the inherent tendencies towards conservatism and discomfort with change, any change, that are deep-set parts of the human mentality. People who are essentially comfortable here and today tend to want things to stay as they are, no matter what that state might be. If that means closing one's eyes to tens of millions of unpleasant deaths every year and the ongoing suffering of hundreds of millions more, then so be it. Yet aging and its consequences are not set in stone, and they can be changed through medical research and development. All this death and pain need not continue. That is why it is important to dismantle the half-hearted and ill-thought objections to treating aging as a medical condition and thereby extending healthy life spans. Most of the death and disease in the world could be swept away in the decades ahead, given the support and investment to do so, but today so very much of that support has instead buried its collective head in the sand.
Arguments against rejuvenation only sound reasonable because they appeal to our fears and to the blame-the-humans attitude of so many people. If you trust only your gut feelings and don't bother examining facts and data, anti-rejuvenation arguments can easily seem obviously true. Accepting an anti-rejuvenation argument requires far less mental work than understanding why the same argument isn't as sound as it appears, but that doesn't make anti-rejuvenation arguments any more 'obviously true' than their rebuttals. It is impossible to know for a fact whether or not rejuvenation will cause any given problem before we get there.
Proving that no problems will arise as a consequence of defeating ageing is not the point of rebutting objections to rejuvenation. That's not what any of my answers does. All they do is showing that objections to rejuvenation rely more often than not on fallacious reasoning, ignorance, fears, misconceptions, and wrong assumptions taken for established fact. In short, what we do when rebutting objections to rejuvenation is showing they aren't valid reasons to let ageing continue crippling and killing us. At the same time, answers to objections show why all those predictions of doom and gloom aren't as likely as they may appear. There's no certainty to be found anywhere, but this doesn't really matter-had we refrained from doing anything that wasn't proved to be 100% risk-free throughout history, we'd probably still be living in caves.
Remember: Objections to rejuvenation are about hypothetical future problems that are far from being certain. Ageing and all the suffering and deaths that come with it are a very tangible fact, happening here and now. This alone should be sufficient to forget about objections altogether and focus only on putting an end to ageing. However, rebutting objections has also another purpose: It fuels discussion. Apart from raising awareness of the problem of ageing and the feasibility of its defeat, discussion prepares us to face the new challenges an ageless future might bring. The way to a world without ageing is still long, which gives us all the time we need to prevent eternal dictators, overpopulation, and all sorts of dystopian scenarios from ever materialising.