Thought experiment: Lets say you live the life of a random human throughout all time, both past and future. That is one data point, but one data point can tell us quite a lot still. So lets say you start your life, and you notice that the human population had just expanded exponentially to 100 times what it usually was, what would you assume will happen in the future? If the future will hold millions of years with hu…
I don't think this logic applies to the demographics of today. The total number of humans to have ever lived is calculated to be ~105 billion. So assuming you're applying that logic to today, you're one of the most recent ~7%, which doesn't seem that remarkable -- at least not to the point of assuming fatalistic scenarios.
But you are right, civilization lasting another few thousand years isn't that improbable. Just that it is strange that it would last a thousand years but not a million, seems like humanity should have figured out how to stabilize things if civlization lasts that long.
Edit: Or maybe our ultimate downfall will just be lack of evolutionary pressure so at some point nobody can sustain civlization. That wouldn't happen in a thousand years but a million years is definitely enough.
Edit2: Or we solve our lifespan issue very soon and people no longer die, so people also no longer can procreate or they would exhaust available resources.