There are two reasons why I believe aliens visit Earth.
One the universe is so damn big that something should find us.
Two the government's excuses are so god damn lame that they must be hiding something.
OK, but why do you believe there are aliens that are more advanced than we are?
Here is a question I have been wondering recently. We see in various SciFi stories (Contact and Explorers being two examples) that our radio and television signals leaving Earth should be able to be picked up by aliens. Anyone sitting within 100 ly of Earth should be able to detect our transmissions.
Wouldn't the converse be true as well? Shouldn't it or wouldn't it be possible for us on Earth to detect "primitive" radio and television style transmissions from other planets? Wouldn't we detect these signals first (unless said aliens have FTL capabilities)?
IDK if our (or their) old radio transmissions would really actually get out that far.
But I think people who say that Earth can't possibly be visited, are kind of ignoring the concept of random chance. Yes, the universe is VAST, and there are countless stars in it. But consider our own Hubble Deep Field survey... the Hubble was pointed to a purely random spot, in the southern sky, and look at what we saw from that. What if, just what if, WE are the absolutely random blotch, to the aliens? What if, by some astronomical happenstance, some alien astronomy team just pointed to some section of the sky at random, and that section of sky just happened to contain our solar system? It is highly unlikely, yes, but NOT impossible.
Or maybe finding Earth was an accident for them... maybe sometime way back, an alien ship was damaged, and had to come out of FTL, or whatever, and just happened to come out in our solar system, and find that there was a world with life on it, and reported that back to their people. Or maybe there was just some kind of alien survey mission, where they were mapping a new area of space, and discovered Earth that way. The point is, that there are many reasons why Earth could be discovered by a starfaring race.
Thing is, because the universe is so vast, and has so many bajillions of stars in it, no matter how far and long you travel, you are statistically going to come across something, sooner or later. If you have advanced FTL ability, and the means by which to scan for Earth-like worlds, those chances increase even more.
In this day in age, nobody will be able to prove that aliens exist... if we see a clear video, we say that it's Hollywood CG effects, or some talented kid with Photoshop. If we see an actual alien beside a human, again, unless we can touch it, or slice it open, people will say, oh, it's Hollywood CG or a great makeup job. Nothing short of a UFO crashing through someone's apartment in the middle of a big city, will convince anyone.