As Douglas Adams wrote, “Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.”
We've been looking for alien life for, what, 50 years? And we've made various assumptions about what we should be looking for. Oh, and we've been doing so on a very limited budget, with the technology available to us, in a tiny part of the sky .