whilst fermi was a clever chap, partially responsible for the a-bombs now in the hands of
nations associated with terrorism, certain data were not available to him in his era:

• if the probability of space-faring civilizations in this galaxy is .000001
• if the mean distance between them is around 50 - 150 light-years
• excluding 10,000 light-years from galactic core, which is also lethal, even on planets
• neither they nor humans can survive interstellar travel
• neither they nor humans can produce a directed communication beam of sufficient power

hence it's not a paradox, any more than the usual aristotelian fallacies propagated by superstition
and whatever else they were mis-taught in grammar school.