I don't even think of it as choosing to believe that we've never been visited by extraterrestrial intelligence. It's that I've never seen any convincing evidence. It might have happened, but if it did, the aliens didn't leave anything that couldn't be explained equally well by a whole long list of other, more mundane, events.
"Now everyone was giving her that kind of look UFOlogists get when they suddenly say, 'Hey, if you shade your eyes you can see it is just a flock of geese after all.'"
"You can't erase icing."
"I can't believe it doesn't work! I found it on the internet, man!"