ETA: or the copernican wrap-around: "Any random person is more likely to be near an average size than not, so...[five dubious steps later]...obviously aliens are mostly going to be average human-sized."
But I will say this is based on entirely reasonable assumptions and observations.
It's an interesting argument as I've always been of the opinion that life is abundant but the universe so large that it's still quite spread out.
This is basically my optimistic/pessimistic view of alien life. The scale of the universe means the probability of alien life existing must be essentially 100%, while the scale of the universe also means the probability of any life finding another instance of life must be essentially 0%.
Although a fun corollary inspired by the Big Alien thought experiment is that local maxima must also exist: Somewhere, some planet with intelligent life must have been close enough to another such planet that they did indeed find each other.
It would imply that the average planet is less detectable than our own planet and thus the Fermi-Paradoxon is resolved from our perspective. Lots of life absolutely everywhere but most of it is undetectable.
Of course this is only about our perspective, the assumption is that aliens would never visit us. So one step further, bigger populations correlate with ability travel. (pulled out of nowhere) However, if they are advanced enough to visit us and therefore have a bigger population than ours (interplanetary species), wouldn't they run into the opposite problem? They would have trouble detecting us because we only live on a single planet.
Interesting point. It follows that as we can observe how galaxies and clusters form, it must follow that if life requires a star, it would cluster and group similarly, and eventually group closely enough for two intelligent species to bump into one another.