How do you justify government hiding information about aliens/otherworldly beings

Well, there is one thing to consider. Suppose aliens are visiting Earth for some reason and establish communications with one government, for the sake of the argument let’s say it’s that of the USA. There isn’t one player here (the government), but two – you also need to factor in aliens have an agency.

A government just figured out there are aliens out there, watching down on them

In other words, if aliens visited Earth, they’re likely to have an agenda of some sort. They aren’t here randomly, or powerless refugees or whatever. They’re here to do something with someone and they chose to contact this particular government and not reveal themselves to everyone. Presumably they could do so at any time, but they opted to do something different for whatever reason.

Taking this further gives a straightforward answer: because it’s more advantageous for the government to keep communications secret. Maybe aliens are after something we can easily part with. Maybe it’s anchovies, maybe pickled anchovies taste like heaven to them and they’re willing to part with technology to produce energy sources sufficient to traverse the stars for a moderate supply for a condiment fish that costs a buck per jar. Plus their oil makes for perfect lubricant for their machines and never needs replacement so they will pay anything for a single can. You do not want that to leak out, so you keep it quiet.

The same goes for anything else they might want. It is not difficult to imagine scenarios where a government keeps alien contact quiet for various reasons, technology being the obvious first try.

Keeping it under wraps for a prolonged period of time is different matter of course. Concealing that knowledge for a year or two is on the very edge of possible.

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I assume you are talking about aliens from a different planet.

Two situations are possible:

1. Aliens exist and have visited earth
2. Aliens exist but have not visited earth

If the first situation is correct then there are these possibilities:

1. The aliens visited long ago creating our god myths. They haven’t been back since.
2. The aliens visit us and we don’t know about it. I presume they have better stealth capabilities than we have and they feel they don’t have the right to interfere with our development – something like Star Trek’s Prime Directive.
3. The aliens visit us and ‘authorized people’ are hiding knowledge of this.

Let’s assume that 3. is correct. What possible reason could ‘authorized people’ have?

a. Maybe they feel they are protecting us from the knowledge that we are not the most superior beings in the universe. Unlikely because secrets like this just can’t be kept. Once there are 50 people aware of a secret it’s been proven that knowledge of it will get out.

b. Maybe they made a colossal mistake and shot down a UFO. They are now scared of our reaction. Unlikely since the Roswell incident happened so long ago (70 years) and few responsible are even alive now. It also doesn’t say much for the alien technology that they could get across interstellar space but get shot down by primitive savages.

c. Maybe they found a crashed UFO and are using its technology to develop super weapons. Again this is unlikely because you don’t cross light years of space and then not have the technology to avoid a crash.

d. Maybe the aliens are benign and here to help. They’ve asked the ‘authorized people’ not to reveal their existence because they feel it will damage us in some way. Unlikely because (2) above would apply and (a) above would reveal the secret.

e. Maybe the ‘authorized people’ are deeply religious and believe that revealing the secret would destroy faith in their god. They have asked the aliens to go away. Again unlikely because of (a).

If we discount 3 as being unlikely AND we’ve been visited by aliens then 1 and 2 are left and ‘authorized people’ simply don’t know any more than we do.

By far the most likely scenario is that supported by Occam’s Razor which states:
If there are several possible ways that something might have happened, the way that uses the fewest guesses is probably the right one.

In that case the most likely scenario is that aliens exist but have not visited the earth.

Your ‘authorized people’ are probably laughing that you believe they know something that you don’t.

Of course there’s one other possibility – that the story about the aliens is a hoax used by government to distract people from some other thing they want to conceal such as the development of stealth technology or new weapons. In this case both the government and the aliens the government doesn’t know about are laughing at us.

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Since you worded it “What reasons COULD,” I shall answer with ten possibilities that instantly come to mind…

1. Because the government itself is already controlled by aliens (duh);
2. Because the government has made a deal with the aliens to supply them with humans for testing/slaves/lunch (double-duh);
3. Because the evidence is in the form of alien corpses that by sheer bizarre coincidence look identical to human mythological imagery of Satan/demons, and could thus prompt widespread religious fears and extremism (this one’s for Arthur C. Clarke);
4. Because the evidence is in the form of satellite, telescope, and secret NASA unmanned spacecraft data proving a primitive alien race on a nearby inhabitable planet that the government has already selected for human colonization, in a secret project to evacuate a portion of the human population prior to an imminent collision with Earth by a massive asteroid we have no hope of stopping or deflecting (this fact would also therefore be a separate government secret, so you now have TWO conspiracies to be paranoid about);
5. Because the evidence proves some major religious figure in the past was actually an alien in human form, and the revelation of this information would cause widespread religious fears and upheavals;
6. Because the existence of aliens would be contrary to the belief systems of at least a significant portion of the world population to varying degrees, and would likely be received with great animosity and fear;
7. Because regardless of religion, the revelation of the existence of aliens would be a huge shock to the human population, particularly evidence of intelligent aliens who have been to Earth;
8. Because the government doesn’t want to admit that the aliens have been — in this particular scenario — coming and going as they please while the governments of the world have been entirely unable to stop the incursions or otherwise intervene, suggesting the population of Earth would be helpless if the aliens chose to actually attack at some point;
9. Because the aliens have only been in contact with one specific group of humans on Earth, and they are not from THIS country (meaning whichever country you, the reader, happen to live in), so the government is reluctant to admit intelligent life from another world came here but didn’t want to talk to them;
10. Because the aliens came, saw how we run our planet, and said, “You people suck, we’re leaving,” telling us that all other civilized life in the universe is ashamed of us for how we treat our planet and one another.

Those are the only ones I’m allowed to tell you about.