Many people firmly believe that the US military is actively engaged in covering up any and all reported UFO sightings. They always seem to go out to these sites, check them out and then declare that nothing happened, which leads people to wonder why they bother to go check on these sightings if they always claim that they aren't anything of importance?
Why Bother Checking
Part of the reason is that they want to know if there is an immediate threat to national security. A UFO sighting could mean a misfired missile, a stealth aircraft from an enemy country or even life from other planets. If there are any aircraft being tested in the area, they also want to know what a civilian saw.
The US military is just like any other government agency in America barely hanging on by the skin of its teeth. There are a lot of mistakes made, a lot of decisions not shared with others and a lot of in-fighting. Inevitably, someone somewhere is going to cry "Conspiracy!" And the military doesn't really help themselves by being so silent and even hostile to answering questions. Since it's not their job to answer questions, no wonder they are not all that good at it.
However, in the 1990s, the military declassified information on many experimental disc-shaped aircraft designs flown in the 1930s to the 1950s. Some were cigar-shaped and some were distinctly flying saucer shaped. These airplanes looked remarkably like descriptions of UFO sightings of the times of round or cigar-shaped craft.
Keeping Secrets Secret
Although it could have saved a lot of fuss if the military had just admitted where the secret Air Force bases were, then they wouldn't be secret anymore. Most military institutions work best with a certain degree of paranoia, hence the strict policies on keeping military secrets on classified information, such as the National Security Act of 1947.
Also, it is not the military's job to prove that America has been visited by extraterrestrials they just want to know if there's any danger to the country. In that way, they do like that some Americans view them as enemies in an elaborate cover up of UFOs. The military can barley cover every soldier enlisted with proper equipment, much less manage something as remarkably efficient as a decades-long cover up of any sort. Soldier's salaries are not large; some soldiers somewhere down the line would have spilled the beans to the better-paying private sector if there were any beans to spill.
Thinking that the military is involved in an elaborate cover up about UFOs by being one of the major investigators of UFO sightings can distract people from much more important problems in the government. It is a sign of a reasonably healthy military that they do not automatically shoot anyone who charges them with conspiracy to cover up UFO sightings.