The apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations and the lack of evidence for, or contact with, such civilizations.
My Resolution to the Fermi Paradox:
Maybe they are here... But just don’t reveal themselves?
Star Trek - Prime Directive
General Order 1: "No starship may interfere with the normal development of any alien life or society." (TAS: "The Magicks of Megas-Tu")
General Order 1 is also better known as the Prime Directive. It supersedes all other laws and directives, with the exception of the Omega Directive.
"Who Watches the Watchers" - Star Trek Episode
In the Star Trek episode "Who Watches the Watchers", part of the crew have an invisibility station they are using to observe a bronze age civilization on a remote planet. When the power station overloads and goes down the invisibility shield wall stops working, and their station is accidentally revealed to a member of this bronze age civilization. I won't ruin the entire episode for you, but the basic premise is that once an alien race reveals its existance, you can't ever go backwards. It's an irreversable decision, and it often results in completely #*@&ing up the more primitive civilization they make contact with.
Advantages of non-intrusive observation
Allows for the unmolested study of nature
Never completely fool-proof
What happens when the cover is blown?
The Catastrophic Implications of Contact with an Advanced Civilization
Native Americans vs. Europeans (a case study)
History teaches us what happens when a technologically superior civilization comes into contact with a technologically inferior one. Things usually don't turn out too good for the technologically inferior, in fact they usually end up having their culture and identity destroyed and being absorbed into the advanced culture.
The Incentives for Governments to cover-up the information
What would the Government gain, or how would they benefit from disclosure (assuming that they have made contact with ETs)? On the contrary I think it would be an issue of national security, since how could you reveal news like that and sustain peace and order? Orson Welles' "War of the Worlds" radio broadcast, is a prime example of how the public could possibly react. There would be no soft way to break that kind of story to the world. On the contrary it would be much easier and safer to keep everything a secret.
Humanity’s need to make this next important step in our evolution independently
Some have argued that Humanity needs to make the transition to a type 1 civilization on their own, and that it would be cheating if ETs came down and just gave us all the technology. For a variety of reasons I tend to agree with this thinking. For one I understand that we live in the most opportune time that has ever existed, and more important discoveries will be made in my lifetime than the thousands of years of history that came before. I believe that humanity can overcome our problems and succeed in making this crucial transition. I want the satisfaction of helping us do it.
While not specifically recommending a cover-up of evidence of extraterrestrial life, Proposed Studies on the Implications of Peaceful Space Activities for Human Affairs does suggest that contact with intelligent extraterrestrial life (or strong evidence of its reality) could have a disruptive effect on human societies. Moreover, it does mention the possibility that leadership might wish to withhold evidence of extraterrestrial life from the public under some conditions.
Does intelligent life exist on other planets?
Absolutely it does! It would be mathematically improbable for it not to.
Can they get here?
It's possible yet difficult given the distances considered, at least without some sort of advanced warp-drive technology.
Would they want to come here?
I would say yes. We would be fascinated if we found other intelligence lifeforms and we'd undoubtedly be interested in studying them and seeing what we could learn scientifically.
Would they show themselves?
Probably not. They would likely have contact and engagement protocols, like you see in most sci-fi tv shows and movies. They can learn far more by studying us uninterrupted in our natural state.
Would the Government tell us?
Absolutely not. Of all the questions on this list this is the one answer I am most sure about. The Government will never ever disclose the truth about ETs.