I think GP is referring to the idea that there are a lot of (unlikely) conditions that would all have to turn out to be correct in order for there to be aliens. Not that there is evidence of no aliens, but that you can do thought experiments to guess at the probability that there are, and it doesn't look good.
Things like:
* There have to be enough star systems and planets that could support life. Research here is exploding as we discover more and more exoplanets and are able to gather more detailed information about them. But it's still not clear that it's at all common, and might be breathtakingly uncommon.
* Those star systems and planets that could support life have to actually spawn life. And then they have to spawn intelligent life capable of creating and using tools, and capable of intellectual thought and developing theories and application across physics and engineering. This life needs to be somehow "compatible" with humans, in the sense that it can't be so wildly different that they might not recognize us as intelligent life and vice versa.
* The aliens have to exist "right now". A civilization that existed in the past and fell even a few thousand years ago is not one that we would see. Similarly, a civilization that is, say, 10 thousand years behind us, is not one that we would see.
* These aliens need to actually be interested in the possibility of life outside their own world (or at least interested in generally exploring outside their solar system), and mount a campaign to search the skies and look for us.
* Then the aliens have to have found us. That means that they have been looking in the right spot, at the right time (aliens who live 3000 light years away won't see "us", absent some sci-fi faster-than-light viewing device). Also consider that the amount of effort we've spent to search for alien life could easily be insufficient to find any, even if life turns out to be somewhat common in our galaxy.
* The aliens have to have figured out interstellar travel. Our current understanding of physics suggests that this is Very Hard. Assuming our current understanding of physics is correct, it will be expensive and difficult for these aliens to come visit us. Even assuming we don't have the whole picture when it comes to physics (almost certainly true), that would seem to increase the barrier, not reduce it.
* Even if aliens do manage to find and reach us, they have to either a) want to be seen, or b) screw up and be seen by accident. If they want to be seen, then presumably they'd have done a better job of it (despite various Earth governments trying to hide it) and detailed knowledge of alien life would be common. If they don't want to be seen, then a -- perhaps unlikely -- accident must occur that reveals themselves to at least some of us (whom the rest of humanity don't really believe).
That's just a taste; there's a lot more you can find if you go down the rabbit hole. All of this has to work out for it to be the case that aliens have visited our world. If we assume that each of these events is fairly improbable on their own, than the probability of all of it happening is pretty tiny. Even if we assign decent odds to many of these things, the probability of all of them being true is still fairly low. Doesn't mean it definitively hasn't happened, but probability it usually pretty suggestive.