Governments may desire to conceal proof of contact with extraterrestrial life for a variety of reasons. Among them are the following:
Governments may be concerned about national security because they believe that if the existence of aliens is made public, it may spark fear or unrest or give other nations a leg up in the arms or technology race.
Governments may be worried that the disclosure of alien contact may result in job losses or a downturn in the economy.
Governments might be afraid that the reveal of alien contact might put people's religious convictions in question or cause societal upheaval.