Be that as it may, that's still an irrational reaction. We don't know what the odds of intelligent life are, and there's no guarantee that they are not comparable to the size of the universe... or even a long shot despite the size of the universe.

For all the stars in all the solar systems in all the universe across all time, for as large as that number may be, you start stacking together independent requirements for life (galaxy with available stable orbits, water planet, habitable zone, mineral abundance, perhaps big moon, and this is the tip of the tip of the iceberg for feasible potential requirements) and the odds against can go up fast, too.

As an example, it is hypothesized that only a spiral galaxy can support life, since only a spiral galaxy will have orbits that are not too close to the galactic center at some point. (Recently, there have been some suggestions that it may also be important not to be too far from it, either.) Right off the top, this eliminates a gigantic number of galaxies from contention. Certainly it leaves roughly an equal number still in contention (couldn't find precise frequency counts but 50% is close enough here), but even the mighty size of the Universe can't sustain an indefinite exponential culling.

We still don't know. Just because there's a really big number on one side of the question that's visibly obvious, doesn't mean that a much more subtle but equally large number doesn't lie on the other side.

(To save time, I've assumed "life as we know it". Feel free to substitute some other definition, though personally I'm yet to see a very convincing argument in favor of non-carbon, non-water intelligent life. YMMV.)

Please be clear: I am not advocating the "we're alone" position. I'm advocating the "we truly don't know" position. There's a difference.

(It may seem trite and old now, but I still think the Fermi Paradox is one of the most important questions of our time. The silliness of the Drake equation sort of got in the way, but it can be boiled down to: If intelligent life is easy and there's no terribly compelling reason why intelligent life can't at least populate the galaxy, why hasn't it? Note that "populate the galaxy" may and probably does take the form of some form of machine life, but I've seen no compelling reason to believe that's impossible yet.)