Humanity is unaware of the existence of the supernatural because the Earth is a massive experiment charting the growth of civilization/technology in a world devoid of supernatural elements.
It is feared that a revelation would send humanity into a massive panic and lead to chaos and conflict due to irrational fear or misunderstanding. Plus, once the cat's out of the bag, it can't be put back - better safe than sorry.
The discovery in question functions as a delayed-action Logic Bomb, driving those that know it crazy over a given span of time.
The discovery of magic includes mind control spells. Even if excluded they could be found easily. It would effectively mean the end of free will for 90% of the population.
The Hidden Elf Village remains hidden because the human kingdom is a greater threat to IT than it is to the kingdom.
The magical wards that prevent Muggles from noticing the Wizarding School break down, but rather than the expected mass panic, people are more excited about it.
The world could deal with it just fine. The secrets are being kept for purely selfish reasons. The Men in Black would rather be reading and controlling minds with alien technology than curing brain cancer and unlocking human potential.
Double Subverted: But once they find out that no, not everybody can attend and get the gift, they get upset and turn on the school.
A Mad Scientist's boss has got so used to his inventions uprooting society that he keeps him in a dungeon and covers up everything he does out of paranoid terror. "The World Is Not Ready for horseradish sauce in squeezy bottles!"
Zig Zagged: There are multiple things the world is not ready for, and different reasoning behind each of them. The rationale for the wizards remaining hidden is based off decisions that predate the industrial revolution and mankind IS in fact ready for them, the reasoning behind Reed Richards being useless is that his discoveries would render entire industries obsolete, putting millions out of work. Vampires are keeping themselves hidden out of fear of Van Helsing Hate Crimes and their need to feed on blood, and people encounter aliens all the time, but suffer Laser-Guided Amnesia afterward because most alien races are jerks that don't consider humans advanced enough to have the knowledge.
Averted: No one tries to keep the discovery a secret. Mankind either acclimates readily to it, or doesn't consider it that big of a deal.
Enforced: Status Quo Is God - While people would probably adjust reasonably well to aliens amongst them, the world that would result would be difficult to portray on the show, and we're not trying to show that anyway, we're just writing a comedy sitcom about a slacker alien living in this guy's basement...
Lampshaded: One of the characters says something along the lines of "Let me guess, we're keeping this a secret because 'The world is not ready', or something like that?"
Invoked: The Secret Keeper invokes this trope due to a somewhat misanthropic viewpoint.
Exploited: The aliens notice that the Men In Black are too secretive to spread even their self-developed energy weapons or even scale it up beyond hand-building every weapon. They go all out and conqueror earth knowing that they won't be able to scale it up.
Discussed: The scientists at a secret government research lab regularly have break-time discussions about their projects getting shut down for this reason... betting pools are formed.
Humanity discovers FTL radio and travel and learns about their world's long and rich history of being screwed with, invaded and nearly destroyed by aliens. As a result, mankind becomes extremely untrusting of galactic civilization at large.
Humanity was meant to be kept in the dark, by ignorance or force, since they are inherently a curious race, and if they were able to utilize FTL travel to it's fullest, the universe itself would be doomed by the evil forces humanity would accidentally release.
The Men in Black are shown to have a long-term gameplan, slowly drip-feeding humanity with alien technology so they have time to adapt to it instead of trying to keep everything hushed up forever.
Plotted A Good Waste: The normal Men in Black organization that the Five-Man Band goes up against on occasion is shown as being competent enough to handle the threats in question and more concerned about the public, however they remain Locked Out of the Loop.