First, he meets an alien who boarded a truck that was pulled over by Border Patrol. BP subsequently witnesses a fight between him and the alien. He wipes their memory. Next, he goes to a farmer's wife's house to interview her regarding an alien's takeover of her husband's body, which he heard about from a public newspaper. He neuralizes her, too. Then there's the stuff with the medical examiner.
My point is, why not leave the memory intact? Fear of mass hysteria?
The judgment (of MIB) is that the population couldn't cope with knowing how the universe actually works, that it's filled with super-powered aliens capable of destroying the Earth at a whim.
As K says, the fear is that there would be mass hysteria. In the novelisation (based on the original screenplay) Kay lays it out for Jay.
Kay nodded at other people in the park. "That old man with the dog, those two women pushing baby carriages, they don't know, either. See it would wreck their worldview to know. Most people can't deal with the naked truth."
"People are smart, they could handle it."
"Wrong. A person can be smart, but people are dumb. Clump people together and spook them and what you get is a mob. And a mob is only as smart as the stupidest person in it."
and
"Listen up, Sparky, there is always an alien battle cruiser or a Korlian death ray or some intergalactic plague about to wipe out life on this planet. We stop it. We've always stopped it, and I don't plan on screwing up this time. The only thing that allows people here to get on with their lives is that they don't know about it! How do you think they would feel if they knew? There'd be a panic that would trash half the planet and cause thousands, maybe millions of deaths!"
The film transcript contains similar exchanges...
KAY: Not as many as you'd think. Humans, for the most part, don't have a clue. Don't want one, either. They're happy. They think they've got a pretty good bead on things.
EDWARDS: Why the big secret? People are smart, they can handle it.
KAY: A person is smart. People are dumb. Everything they've ever "known" has been proven to be wrong. A thousand years ago everybody knew as a fact, that the earth was the center of the universe. Five hundred years ago, they knew it was flat. Fifteen minutes ago, you knew we humans were alone on it. Imagine what you'll know tomorrow.
and
KAY: There's always an Alien Battle Cruiser...or a Korlian Death Ray, or...an intergalactic plague about to wipe out life on this planet, and the only thing that lets people get on with their hopeful little lives is that they don't know about it.
As per the Men in Black wiki page, in 1961:
It was decided to make Earth an apolitical zone for aliens without a planet, and the organization broke its government ties to become the Men in Black, which became the singular force to conceal and police the aliens that came to Earth
From this, we can conclude that if aliens are trying to seek political asylum, they ought to be left alone. If the public became aware that extraterrestrials did exist, yes, there probably would be mass hysteria and potential specie-prejudice arising against these individuals seeking asylum.
Also, the fact that the organisation split ties with the government means that if we had a large number of people with intact memories of aliens, there could be seriously negative consequences. If the government became aware of this, it could result in negative relationships being established with other alien life-forms; without the knowledge of the actions of the Men in Black organisation, Earth could get itself into some seriously deep trouble!
Another aspect to consider is that a lot of the encounters people have with aliens are not pleasant memories; consider the wife whose husband was killed; if you could forget something scarring like that, you probably would want to.
Because humans finding out that not only are we not alone, but that there are actual interstellar aliens living on earth and walking among us would cause a mass panic. K says it best when sitting on the park bench with J, explaining the situation to him. J asks K “why the big secret? We can handle it, people are smart”. K responses with “A PERSON is smart, PEOPLE are dangerous, panicky animals and you know it!!” Basically, humans haven’t evolved past the mob mentality yet, and just a few people freaking out and wanting to go on an alien killing spree would trigger a mob of alien murders. If a super advanced race like the Arquilians (who already don’t like us very much) would have one if theirs killed, they’d evacuate the rest of their race and destroy earth.
civilian who saw an alienis not neutralized. Lots of people are allowed to see aliens and go on with their lives. Rather those who witness MiB interactions relative to aliens are neutralized. – user2338816 Jun 21 '15 at 4:40