We don't have to prove Aliens exist for the same reason we don't have to prove God exists. If we want to believe, we can. If you insist they do not exist--not simply by stating that, "I faithfully believe that they do not exist," then you must offer proof. Otherwise, you are guessing just as much as we are, and exercising personal faith.
I don't know whether aliens exist or don't exist. I crave tangible evidence. But I want to believe, and I'm okay enough with that.
Thanks for supporting my main point that belief in extra-terrestrial life and belief in a "god" are both based on faith due to the lack of hard empirical evidence.