Punk at its inception was all about free love and mosh pits. They promoted sex, drugs, and screaming at each other. Lyrics were about bucking the system and beating people (often yourself) up. But it was all high-energy and very often done in satirical and funny ways, if you could get past the squealing guitars and eardrum-bursting volume to understand them. Most bands were self-consciously crossing every line they could find and laughing at themselves for it. Just look at some of the band names The Circle Jerks, The Queers, 999, the Buzzcocks (whose most well-known song is Orgasm Addict), and the Dead Kennedys. And you're probably at least a bit familiar with some bands you don't think of as punk at all Blondie, the Talking Heads, and Devo for instance.
Punk has been around for over 30 years and has changed drastically over the years. It is, however, still struggling to breathe. Bands like Suicidal Tendencies, Nuclear Rabbit, L7, and Rancid have hauled the genre through the 1980's and 90's, trying to keep it alive. Even though it's harder find pure punk these days, it's still out there if you know where to look. Try some extreme sports video games and discover bands like Pennywise and Bouncing Souls. Like any other genre, there are sub-genres and even individual tracks you can appreciate without having to learn to love the Sex Pistols. How could you not enjoy The Ramones? My 5-year-old's favorite song is Blitzkrieg Bop! The focus is not on looking good (well, for good music it isn't) but on finding a way to poke fun at yourself and the world while protesting everything from your parents' choice of carpet to your government's decision to go to war.
There are a lot of good things to say about punk along with the bad, and you can't lump the entire genre into one screaming, slamming mass. While this has been more of an introduction than an analysis, it should provide some guidance for those who are interested in the subject but don't know where to start. Take an open-minded listen to The Clash (maybe Julie's Been Working for the Drug Squad or Tommy Gun) and The Damned (BeatBeatBeat, perhaps) and give them a chance. Sure, there are some very violent and disturbing songs out there. You just have to remember that there are disturbing songs in any genre and work around what you don't like. And if you just can't find it in your heart or your ears to like punk, try some ska. You get a lot of the same things, only with a brass section.