I can easily see 2 things wrong with the doomsday argument. First, the same rule has to apply for the person #10 000, for example. If they thought of themselves as a random sample, it would be very unlikely that they would live in a world, where people would reach numbers like 100 billion. Yet, the person #10 000 happened to be indeed in a world, where people actually reached #100 billion. Second, we don't need to reproduce and multiply in this same old biological way forever. We may indeed be some of the last humans to ever be born, because we might discover how to reverse aging and even upload our consciousness into machines, so we can live forever and no need to reproduce.