This argument is called the Doomsday Argument. It has been discussed several times around these parts (e.g. here)

In a technical sense, the issue resolves around how you think self-sampling should be understood. You might consider looking up the "Sleeping Beauty" problem for more discussion of that point.

In a non-technical sense, there's what might be called the "reference-class problem." On the one hand, the number of people in existence has constantly been increasing over time. On the other, the number of interconnected civilizations seems to be dropping (after the widespread adoption of the internet, one could argue that the number of distinct civilizations currently in existence can be counted on one's fingers and toes). Figuring out the correct reference class has profound effects on the conclusions one reaches using this kind of reasoning.