The explanation I have heard repeatedly goes something like:
"This equation shows that there should be [massive number] of alien civilizations in the universe. But where are they?"
This seems to assume that, given the density of civilizations throughout the galaxy we can determine from [massive number], we should be able to observe other advanced civilizations. But is that true? If there was a civilization as advanced as we are somewhere in e.g. Alpha Centauri, would we be able to detect them?