Song lyrics tend to run the spectrum as far as evoking emotions. Some songs are just plain mean.
Morrissey - It's Not Your Birthday Anymore
Fountains of Wayne - Waitress
Trey Parker - Pearl Harbor
Steely Dan - Reeling In The Years
John Lennon - Crippled Inside
Have another drink and drive yourself home.
I hope there's ice on all the roads.
You can think of me when you forget you're seat belt,
and again when your head goes through the windshield.
"Me vs. Maradona vs. Elvis" - Brand New
I will lie awake, and lie for fun and fake the way I hold you.
I think the difference is that anger is often justified, while meanness never is (as satisfying as it might be at the time). Early Dylan offers a lot of fascinating examples of that dichotomy - his social/political songs are frequently angry ("Masters of War", "The Lonesome Death of Hattie Carroll"), while his interpersonal songs (like the already-mentioned "Don't Think Twice") are often just plain mean.
BillAdama cited Lennon's "Crippled Inside", but I've never heard that particular song that way. It's more of a general statement of purpose/warning, directed at the universal "you" (including, no doubt, Lennon himself) rather than at anyone in particular. Now, "How Do You Sleep?" on the same album - THAT's mean. (Again, the same dichotomy: "I Don't Want to Be a Soldier" - angry. "Gimme Some Truth" - angry. "How Do You Sleep?" - so mean, it's a wonder its subject ever spoke to him again, although that relationship had depths and complexities that will probably never be fully understood.)
Great PJ Harvey example (it's hard to think of a more cutting thing for a woman to say to a man than "You leave me dry"), but RID OF ME has a track that's even meaner: "Rub 'Til It Bleeds", which is essentially "I Know What Boys Like" with all the humor and hooks stripped away so that only the ugly taunting remains.
How Do You Sleep is the perfect mean song. Not angry. It has a little anger, but it practically drips with madness. I also agree with Harold that we'll never understand the Lennon-McCartney relationship. Their relation to each other is actually unique; you can only have one "greatest song writing team of all time".
As for angry, Masters of War and every heavy metal song are good for that.