The Fermi Paradox. For those unaware, the Fermi paradox is simply stated: Everything we know about life on other planets tells us that life should be commonplace across the stars and we should be able to see evidence of alien life. (Corollary, life should be common enough that we shouldn't have had time to develop before our planet is colonized) The problem comes that we don't have any real evidence that alien life exists. There are a few sightings that might indicate alien life, (Weird telescope sightings of other star systems that would theoretically indicate intelligent life, not the aliens in Roswell type) but they're slim and nebulous. Life should be everywhere, but we see none of it. Some sort of Great Filter stops life from being visible to us, or even existing. Therefore, the next step when talking about the Fermi paradox is to discuss why we don't see any signs of intelligent life.
Personally, I find that your reaction to this problem is the interesting bit. There's a whole host of possibilities for why our observations are different from our expectations, and little data to work on. Therefore, your thoughts on the cause are likely to be inspired by thoughts outside of this specific problem, which is why I find it fun. It's a science fiction Rorschach test, if you will.
I find it useful to split possible solutions to the paradox based on whether they come relatively after or before modern humanity. If the problem is before current times, then it likely means that humanity is special and has already passed the Great Filter. A bit of optimism is required, but also can indicate how you think humanity might be special. You could think that life is special, and exceedingly rare enough that only Earth is lucky enough for it. Maybe you see intelligence as unique, after all, life existed for some 3.6 billion years before humans came around. Maybe even it's something unique to humans where complicated industry to become spacefaring is out of reach? We did spend a long time planet-bound, and extinction level events aren't unheard of.
Problems that the future of mankind will have to deal with are often depressing and pessimistic. Maybe we'll beat them, but the evidence we see amongst the stars tells us that the odds are very much against us. What we know gives us a rough guess of just how many other civilizations have grown and likely run into the very same problems we'll encounter. Maybe you're optimistic that we'll beat the odds anyway, but good luck with that.
What kind of problems are we talking about for the future? There's the ever popular nuclear armageddon where nuclear weapons are developed, and inevitably used to end life on that planet. More popular during the Cold War though, given the circumstances. Perhaps some early idiot made self-replicating robots that kill any species that makes it into space. All it takes is one idiot species. Perhaps we run into societal traps. Is there any real point to colonizing other planets? Much simpler to keep humanity limited in scope so that we can all live comfortably on Earth. Or even better, live in a simulated dream world. No need to expand all that much if everyone only exist as programs in a machine.
There are plenty of other problems that could be a potential killer for spacefaring life. This is by no means an exhaustive list; I'd be here all day listing them if it was. For those that do read this...what do you think is the cause?