I never much liked this being called a paradox since it has so many built in assumptions, most of them centered around any given, theoretical alien civilization resembling a human civilization in any way. It's a limitation of what we know for sure, since there's certainly no rule that civilization elsewhere should resemble civilization on Earth. That's an acceptable limitation, it's difficult to notice things you don't know you should notice, but it's a limitation nonetheless.

Of course, it's also possible for civilizations to be so far away that we will like never detect them due to the inverse square law. They could even be in parts of the universe we can't observe.