What are some songs that seem to capture the author's feelings in a very naked and honest way?
The two songs that come to mind for me are Korn's Daddy, and Dream Theater's Space-Dye Vest.
What are some other examples?

Obviously this will be rather subjective, but to me The Chasm's From the Lost Years sounds very raw, passionate and personal. It's death metal, but definitely unique. I like reading the lyrics, too.

Tool - Hooker with a penis. Maynard is usually a disgruntled person, but here the gloves are off, and targets one specific individual that pissed him off. No subtlety and straight from the gut.

Surprisingly enough, I've found a nice handful of post-metal bands with female vocals who do this incredibly well, namely Oathbreaker and Battle of Mice. In both acts, the frontwomen write the lyrics, detailing actual traumas and sincere feelings that seem to come from pretty deep down.

Oathbreaker - Second Son of R. (a song about being neglected as a child)


Battle of Mice - At the Base of the Giant's Throat (a song about domestic abuse, the end of the song even features a 911 call that was made when the singer was attacked by an ex)

Dude, Battle of Mice is amazing. Not just this song, their stuff in general.