Simply noting that people in the past would have been wrong when they used the Carter argument to predict their own imminent demise doesn't get you out of Carter's bind. It's inevitable that from any vantage point in time we'll see a group preceding us who "would have been wrong". But because of the exponential growth in population, that group is always small compared to the mass of people living today and in our future.
Carter's saying that a small number of people will be wrong to use his argument, but a large number will be right, because they'll be close to the extinction event, or the start of the exponential decline in population - they'll be in the population bulge, where the area under the population curve is high.
So if we choose a life at random from under the population curve, we have a small chance of ending up in the group who are wrong (those in the early days of population growth), and a large chance of ending up in the group who are right (those in the population bulge before the decline).
The way out of Carter's argument is to point out that exponential growth is unsustainable, and if we are to survive we are going to have to achieve population equilibrium. Once the population curve becomes a level line leading off to infinity, we're just as likely to find ourselves anywhere under that line (because there's no bulge to "concentrate lives" in one temporal region), and so we can't infer anything about survival time in the future.
Either we have exponential growth, and Carter's right, and we're likely to be living in the End of Days; or we level out our population, and Carter can't make any deductions about the future - the areal midpoint under an infinite level curve is anywhere.

Grant Hutchison

Edited for clarity, by changing "to use" to "when they used" in sentence 1