No matter how many times I hear this explained, I can't shake the feeling that there is something out there. Whether it be intelligent life or just microbial, there has to be something.
Just because we haven't heard anything yet, doesn't mean there is nothing out there. The universe is just so unbelievably enormous, the distances so vast, that it's entirely possible that some civilization 1 million light years away discovered they could send radio signals 500,000 years ago, meaning it's still going to take another 500,000 years to even get to us. That is, if we can even pick it up due to the distance travelled and the inverse square law. The signal would be degraded so much that we likely wouldn't be able to even detect it.
Or, there could be life 90 billion lightyears away, meaning there is just no way we'd ever receive anything over such a vast distance. If they sent something 12 billion years ago, it's never reaching us. The earth could be gone in 5 billion years or so once the sun says "fuck this shit" and nukes itself.
This is all assuming that these beings use the same communication methods as us. We can't assume that another group of lifeforms took the same path we did. They could be communicating via channels we don't even know about, or perhaps they have no interest in entertainment or communication over distance so things like radio / tv etc just aren't used. We literally don't know, because we've not found anything, so it annoys me when I see people just assume so much stuff and use that as fact to say "well we would have found them by now." - well, you can't prove that, and we need to be open to the fact that there may be something out there.
Love Brian Cox, but not a fan of this paradox and never will be.