"worthless person" (especially a young hoodlum), 1917, probably from punk kid "criminal's apprentice," underworld slang first attested 1904 (with overtones of "catamite"). Ultimately from punk (adj.) "inferior, bad" (q.v.), or else from punk "prostitute, harlot, strumpet," first recorded 1590s, of unknown origin.
For sense shift from "harlot" to "homosexual," compare gay. By 1923 used generally for "young boy, inexperienced person" (originally in show business, as in punk day, circus slang from 1930, "day when children are admitted free"). The verb meaning "to back out of" is from 1920.
The "young criminal" sense is no doubt the inspiration in punk rock first attested 1971 (in a Dave Marsh article in "Creem," referring to Rudi "Question Mark" Martinez); popularized 1976.
If you looked different, people tried to intimidate you all the time. It was the same kind of crap you had to put up with as a hippie, when people started growing long hair. Only now it was the guys with the long hair yelling at you. You think they would have learned something. I had this extreme parrot red hair and I got hassled so much I carried a sign that said "FUCK YOU ASSHOLE." I got so tired of yelling it, I would just hold up the sign. [Bobby Startup, Philadelphia punk DJ, "Philadelphia Weekly," Oct. 10, 2001]