UFOs, the term has come to mean something entirely different in today's world than what the original meaning was. Unidentified Flying Object, that could be a balloon or a helicopter. Until you know positively what it is, it is a UFO. Today when we use the term UFO we mean a "flying saucer" or a spacecraft from another world. Piloted by an alien life form. Why would the U.S. military cover up sightings of UFOs? There are several reasons that they would do this. Some are genuine and legitimate, others may not be. Like any government agency, there is always something that is going on behind the scenes that the general public may not know, or need to know about. They may cover up the reports and sightings because they are responsible for the UFO.
As military technology advances, the aircraft being flown may not look "normal" to an observer. A great example of this was when stealth aircraft was being developed. They didn't look like a traditional aircraft and caused more reports of sightings than can accurately be counted. Why wouldn't the military just come clean with what they are doing? That pretty much goes against what the military's purpose is. The military is used to protect America and it's citizens. Other countries have armed forces for the same reasons. Sometimes two countries will disagree and we have what is called a war.
All sarcasm aside, wars are as old as the human race. We have just upped the ante on them. Usually the person with the biggest (or smartest) weapon will win. If the U.S. has aircraft with advanced capabilities, they don't want possible enemies to know about it. This doesn't have to mean spies and sabotage. If the press runs an article about it, the possible enemy can read about it in the paper just like the American public does. That is not good for the military. The other side of the cover up coin is that the UFOs are the legitimate thing, that is, lifeforms from some place other than Earth.
If this is the case, the military might cover up the sightings on orders from the government (who is their boss). With all the fighting, wars, and xenophobia, people may not be ready for positive proof that there are aliens visiting the planet. It could very easily cause mass panic and a break down in our society. If we just keep it with the military being the highest that it goes, that is the government hasn't ordered them to keep a lid on it, there is still good reasons for potential cover ups. If the military is aware that there is extraterrestrial life forms and they are in fact flying around the skies of Earth, it would be proof that they are more advanced than we are.
The reasoning for this is the simple fact that we don't have the technology to cross interstellar space. The best we have done is land on the moon and send mechanical rovers to Mars. We don't have manned flights around the atmospheres of other planets. There is no guarantee that the alien life forms will be friendly. If they have hostile intentions, the military would need as much time as possible to prepare. A population that is in a state of panic would not help. If by chance, the military has in their possession, one of these UFOs (like the Roswell incident) they could reverse engineer the craft for the technology. It would give the U.S. (and hopefully the world) access to greater technologies that would help everyone.
Humans being human, chances are the first use of the technology would be of a military nature but it would filter down to general civilian use eventually. So basically, why would the military cover up UFO sightings? 1. They are responsible for the unidentified flying objects in the first place. 2. They don't want the general public to know that alien life forms exist and are visiting our planet. 3. If they visit our planet and the military knows, other (potentially enemy) countries may not know about it. That sums up a few of the reasons that the military may cover up sightings of UFOs. Some of the reasons are for the good of the citizens of the U.S. and to an extent the rest of the world.
As it stands, humans are not on the same page. We fight among ourselves constantly. Until we can work together, as a human race, we may not be ready to deal with any form of aliens. Friendly or not, they could pose a threat because of the nature of humans themselves. The military covering up UFOs might be for the right, or the wrong intentions but for now, it could be the best thing to do.