In a 1995 cover story for Rolling Stone, Billie Joe Armstrong explains the origin of the title:

“Brain Stew,” Armstrong explains, is the nickname of James Washburn, a longtime friend of the band. “He used to have a big mohawk; now he’s a total ratchethead [California slang for a car buff],” says Armstrong. “He’ll say something like ‘Oh, man, that guy fuckin’ slipped a gear,’ when someone snaps. He’s a big lyrical influence on me.” And the opening lines of “No Pride” (“I’m just a mutt/And nowhere is my home/Where dignity’s a land mine/In the school of lost hope”) are owed to “Gonna Find You,” a song by another mentor, Jesse Michaels, who led the late, great Berkeley act Operation Ivy, whom Armstrong calls “a punk-rock Kerouac.”

Billie said in an interview with Rolling Stone:

This song is such a dark horse. I had just gotten some recording equipment, and I came up with the riff when I was experimenting with it for the first time: “Oh, this is cool. It almost sounds like a harder Beatles song, like ‘While My Guitar Gently Weeps.’ ” The song is about methamphetamine, not being able to sleep, and staying up all night. It was something that was creeping into our punk scene at the time, and I definitely did my experimenting with it. It’s just such an evil drug.

Things were getting really scary. I’m such a dedicated songwriter and musician, and when Dookie got so big — it was on par with becoming one of the biggest pop records of all time — I really wanted to be like, “I’m a rocker. I’m a punk rocker. That’s what matters to me more than being some kind of pop star.” That sort of fueled that record.

Everything was happening. I got married, I had a kid, I was 23 years old, and people were climbing in my trees to look inside my house. It was the scary side of becoming a rock star, or whatever. You can’t control the outcome of your life. I wanted to show the uglier side of what Green Day was capable of.