Fermi's paradox should, first of all, be recognized as an off-hand remark. That somewhat excuses the thoughtless nature of what Fermi said. First, to look at statistical reasons why the paradox is not really a paradox:
The mere number of stars, and therefore, potential planets in this or any other galaxy is a poor starting point for calculating the probability of technological civilizations. Many of the stars in any galaxy are clustered near the center of the galaxy (i believe that that is probably most of the stars, but am claiming no expertise, and so won't insist upon it). This would mean a high dose of stellar radiation in those areas. The earth is protected from cosmic radiation in general and solar (our stellar) radiation in particular by our magnetosphere and a dense atmosphere. Mars has neither protection, and doses of radiation from solar flares, for example, could easily be lethal to terrestrial life forms, if any were on the surface of Mars and not otherwise shielded. So exposure to stellar radiation is one negatively mitigating factor for the rise and continuance of life, and the odds against the rise and continuance of life must necessarily be higher in the galactic center. Additionally, in the very center of the galaxy, the tidal forces of gravity may well be so great that the odds of the formation and continuance of planets in that region are much lower than is implied by estimates based on uniform distribution assumptions. Statistically, the estimates being used are wildly unrealistic. The probability is that it is only in the galactic boondocks (which is where we live) that stable planets will form and survive, and that life will arise and continue.
The probability of our detecting other technological civilizations has also been wildly overestimated. As this source states
, we have only "looked" at a tiny, tiny fraction of the sky, and are only capable (at present) of "looking" at a tiny, tiny fraction of the sky. It is silly arrogance to suggest that if they're out there, we would have known it. Statistical hilarity ensues.
Statistically speaking, making best estimates suggests that the probability of life arising and continuing and the probability of our detecting other technological civilizations has been wildly overestimated.
Fermi showed himself to be both uninformed as well as naïve in other regards, too. His choice to ignore the implications of stellar radiation is mere arrogance on his part. That he didn't know about the probable effects of micro-gravity is excusable. Sending space craft out with people on them will necessarily require enormous expenditures of energy and materials. What is the probability that a population of sentient, self-aware individuals would endure the sacrifices necessary for that? Our own example is not encouraging. Fermi seems to have envisioned planetary governments with the power to rule by fiat. How likely is that? Fermi showed a distinct lack of imagination.
Without going into more detail, i consider the so-called Fermi paradox to be a sham.