I don't think anybody anywhere really claims that alien life doesn't exist at all, except for some religious folk who think the whole universe was created solely for the benefit of mankind. But the non-religious skeptic of the possible existence of alien lifeforms is a straw man used by UFO nuts to attack people who don't think Farmer Jim-Bob really got an anal probe from a Martian. That kind of skeptic doesn't exist. Nobody says there's any proof alien life doesn't exist, but a lot of us are saying that we just don't see any extraordinary evidence supporting the extraordinary claim of encounters with beings that did not evolve on our planet.

There's a huge difference between doubting the existence of extraterrestrials who are visiting Earth and doubting the possibility of extraterrestrials existing anywhere else in the universe. I think it's incredibly improbable that we're being visited by aliens, but I also think it's incredibly improbable that Earth harbors the only life in the universe.