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One thing we have learned in recent years is that planets are common. That was suspected, but it was confirmed with the discovery of exoplanets. It's easy to detect Jupiter-sized planets, but hard to detect Earth-sized planets. We really have no idea how common life is, but we have discovered that life on Earth can exist in a far wider range of conditions than we had previously imagined. Just about anywhere you look on Earth, there is life. There is life in water hot enough to cook us, life that loves acid, life that loves salt, etc. Dig down miles into the crust, and you will find life in the rocks. I was watching a documentary recently, and it was talking about life on Antarctica. It looks lifeless, but break open the rocks and there is a thin green layer. The algae in the rock is frozen nearly the entire year, but for a few days each year, the rock is warmed enough for photosynthesis to take place.
Fermi's paradox makes another assumption, that an advanced civilization would have a single-minded dedication to spread throughout the universe. It imagines that colonists are sent out, and then that new colony immediately plans to send out colonists of its own. Such ambition makes building the pyramids of Egypt or the cathedrals of Europe look like a child stacking blocks by comparison.
I think we can conclude that no such species exists in our galaxy with an overwhelming drive to grow and spread through the universe. That doesn't mean that technologically advanced species don't exist. Perhaps when they reach a certain stage of advancement, they don't keep growing their numbers.
As Douglas Adams put it, "space is big". We haven't even scratched the surface. What would it mean for intelligent life to be "rare"? There are upwards of 100,000,000,000 galaxies with upwards of 100,000,000,000 stars per galaxy. That is many opportunities for life to emerge. One per galaxy would, I think, qualify as rare. So would four per galaxy. It would still be rare enough that it might be quite unlikely to discover them. But for Earth to be the only planet in the whole universe with intelligent life? Not quite impossible, but I think it would be astonishingly unlikely.
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