He may have been John Cougar or something else in 1983, when this song was made. A #15 Billboard hit, it is an update of I Fought The Law, by the Bobby Fuller Four.
Mellencamp fights authority and authority always wins. He means authority as state power, and maybe the law, as in the police.
Authority is often used interchangeably with power, but more specifically in political science is a certain type of power. Authority in this more formal and official sense is when people follow directives because they respect the givers of such commands. As political communities we have agreed who the authorities are in this sense, such as the government, and its components, say, police officers.
Of course, submission to authority reduces personal freedom. In the song, the narrator figures he’d rather die than grow up and follow orders. This is classic rock and roll rebellion, but in practice, not conducive to social order and safe, predictable living.