I might need a better title (It has now been updated), but here goes, anyway:
I've been considering this for a while now. Suppose we reach a point where we can live for centuries, maybe even millenia, then how do we balance? Even assuming we're as efficient as possible, there's a limit for how much resources we can have, meaning an artificial limit at the amount of people that could exist at any given moment even if we explore what we can of the galaxy and use any avaliable resource. There would have to be roughly the same rate of births and deaths in a stable population.
How would this be achieved? Somehow limiting lifespan, or children, assuming it's available to a majority? Or would this lead to a genespliced, technologically augmented and essentially immortal elite that the poor, unaugmented ones would have no chance of measuring up to? I'm sorry if this has already been considered, I'm very uneducated on the topic. If it has, could someone maybe link an analysis of the topic of lifespans and the like?
The reason why perhaps not push the button: unforeseeable (?) unintended consequences.
I expect point number 1 would weigh heavily in anyone's mind when making the choice, but it might turn out to be a harmfully biased option, assuming it even works. As to point two: in the absence of diseases and aging, the population would hit its limits along some other front. Starvation is only the obvious end of the line; the catch is what we might expect to see on the way there, such as rising global tensions, civil unrest, wars (gloves off or otherwise), accelerated environmental decay - all the things that may not seem like such pressing problems now. We could with perfect seriousness ask the question whether the current state of affairs isn't safer for humanity at large than after pressing the button. (I'll confess: I would use people's answers to the original question mostly as a proxy measurement for their general optimism.)
Frankly, I'd argue the exact reverse of point 3. IMO, it takes heavy speculation to avoid any of the risks I mentioned, and speculating on the positive effects is what seems questionable. The only immediate species-wide benefit would be that world-class expertise on all fields of science suddenly stops pouring out of the world at a steady pace. Anything like "people will care more about the future" supposes fairly fundamental changes in how people think and behave. I expect birth control regulations would be passed, but would you expect to see them work? How would you expect to see them enforced? My guess is: not in worldwide peace and mutual harmony.
Are you also considering the unforeseen unintended consequences of not pushing the button and concluding that they are preferable? (If so, can you clarify on what basis?)
Without that, it seems to me that uncertainty about the future is just as much a reason to push as to not-push, and therefore neither decision can be justified based on such uncertainty.