We are not special. If we are not special then it stands to reason there must be a lot of creatures like us on worlds like this one. So where are they? Where are their radio waves and spaceships? If we discount the wild tales of inbred hillbillies who say that Martians changed their cat's DNA and administered an anal probe to them, then it appears we are alone in the universe.
For those who point to crop circles or to any of the other proofs given out by the tinfoil hat abductees, sorry but Occam's razor easily dispenses with all that so-called proof. Occam's razor says that if you have two equally plausible explanations for something, all other things being equal, the simplest explanation is usually the best. One of the ways we can use to determine whether someone is doing science, or something else, is if he uses Occam's razor over other methods of determining the source of unknown phenomenon. For instance, once you have seen drunken farmers make crop circles, when someone shows you a new crop circle if you use Occam's razor you conclude it's a drunken farmer. If you conclude it's space aliens and provide no other proof, then whatever you are doing it's not science.
By the way, the only kind of proof that is acceptable for space aliens is something truly alien. For instance, all life on earth is based on DNA. If you find something that can be verified in every lab in the world as being alive and not being based on DNA or RNA, then you have a good candidate for an alien.
Some truly alien technology would also suffice. For instance, a device that creates and controls miniature black holes for time travel would be beyond our technology.
So using Occam's razor we assume that each and every person who ever claimed to be abducted by space aliens to be either crazy or a scammer. This is not necessarily true. That's not what the principle says. But it is likely to be true, and in science, that is often the best we can do.
One of the obvious things you could say about the Fermi paradox is that it is wrong. That our planet is ordinary? That our sun is somehow strange?
There are some speculative assertions we might look into having to do with the circumstances we find ourselves in. For instance, even if we are not special, statistically speaking, some world still has to be first in the intelligence sweepstakes. First to use radio waves. First to reach space. Maybe by blind chance we just happened to be first and the others will come along sooner or later.
There is a negative way of looking at these matters. Suppose that most civilizations which get sufficiently complex destroy themselves. This alternative is unfortunately very, very plausible. A world war could wipe out a civilization. A release of viruses from a lab could wipe out all intelligent life. Sooner or later a meteor might strike and wipe out most traces of civilization. A computer virus might be released that destroyed all linked systems. Computers and robots might take over and wipe out their makers.
Suppose there were intelligent space fairing races that decided that they did not wish to be known by others. They might deliberately mask their use of technology. Also, because we use things like radio and TV that spew out energy in all directions out to infinity we assume that other intelligent races will do the same. Suppose they don't? Then we would have no means of detecting them. In this case it would not matter if they use an undetectable means of communication or none at all; we would not know they were there.
The universe is vast and the speed of light is the same to all observers. One of the reasons we might not be hearing from anyone is they are too far away and there just hasn't been enough time yet. There are over 100 billion galaxies in the universe. Galaxies are collections of stars. A typical galaxy contains no fewer than 10 million stars, and as many as a trillion stars. So on the low end of the estimate there are more than a billion billion stars in the known universe. That seems like a lot of real estate in which to find creatures like us on a planet like ours.
Nevertheless, there are scientists who assert what is known as the Rare Earth hypothesis. Basically the Rare Earth hypothesis asserts that the probability of earth-like planets could be as low as one in a trillion. To get there, those who hold this hypothesis posit assertions such as that an earth-like planet must have a large moon to support intelligent life as we know it. Such a specific attribute is a little harder to come by. The proponents tie together about nine unlikely attributes and come to the conclusion that we don't see the aliens because earth-like planets are rare in the universe.