Opposites were first created by a spirt that possessed Aristodemos' body. Since Aristodemos was one of the first Mekahumans, one of the only two to be born instead of gifted, and the brother of the first Meka, he was more powerful than normal Mekahumans.
Since the spirit had full access all of Aristodemos' powers, even ones that Aristodemos didn't know he had, the spirit was able to take a warped version of the Meka's gifting ability and use in to create Opposites.
Opposites, like their name suggests, have the opposite, and sometimes the same, power as the Mekahuman they are tasked with destroying. Their one purpose is to do everything they can to kill the Mekahuman they were meant to be the opposite of.
Opposites follow the same rules of immortality that Mekahumans do, and they also have the flight. Opposites and Mekahumans balance each other out almost perfectly.