My favorite explanation was written by Terry Bisson in 1990.

They're made out of meat!
http://www.terrybisson.com/page6/page6.html

The Fermi paradox is written (understandably) with a very human perspective. We believe that we represent the pinnacle of Universal understanding but in reality nothing could be further from the truth. Our Universal situation is akin to an ancient civilisation stranded on a small island in the middle of the Pacific Ocean. They have no means of contacting the outside world.....they have attached messages to the feet of trained birds and sent them off but to date have received no reply. They've even managed to send a few people to a small neighbouring island and that was uninhabited. Surely if there were other people in the world they would have made contact by now. There have been reports of strange flying objects in the sky but nothing can be confirmed. The leader of the tribe concludes that due to fact that no contact has been made with any other tribe they must be the only tribe on the entire planet. Make no mistake, the only conclusion that can realistically be drawn from the Fermi Paradox is that there is a proliferation of developed, intelligent life out there and we're the primitive tribe looking skyward, scratching our heads.