Since there's an abundance of advice out there on writing songs and step-by-step guides, I thought it would be helpful to go in the other direction on this issue.
It is important in the process of not writing songs to simply not try anything, at all. Merely the writing down of phrases and words can be too much trouble, leading to accidental masterpieces. Just avoid pens and pencils completely. Is that a notebook in your pocket? Throw it away.
When playing instruments, never allow accidents or experiments. A new interval or dissonant sound can lead to all sorts of creativity. This is a terribe way to not write songs.
Listening to the radio? I'd recommend pop stations. Do not turn on NPR. Listening to NPR has given me far too many actionable ideas on song topics.
Don't read newspapers or magazines, or books. One of the most prolific and important songwriters, Woody Guthrie, was an unstoppable researcher and synthesizer of information, famously writing in one night one of the great songs inspired by a novel, the Ballad of Tom Joad (based on Grapes of Wrath). See how dangerous reading can be?
Avoid music conferences -- any number of the Folk Alliance gatherings throughout the year in particular are bad news when it comes to not writing. They are horribly inspiring -- hearing day-after-day of great original music or traditional favorites rendered expertly by friends from around the country can lead to all sorts of song ideas. Bah!
Reflecting on memories or dreams is an awful practice and it is an absolute shame to even consider introspection when it comes to not writing songs.
Do you talk to friends and family, perhaps doing the abysmal practice of hearing them and listening to what they have to say? What a disaster. Our own experiences are terrible, as it is, when it comes to not writing songs. The trials, tribulation, and triumph of others, that's a goldmine of failure to not writing songs waiting to happen.
Are you human? Survey says, X. Yeah, I know, that's an area we can't readily change...but when the technology is available, I'm sure we'll be able to upload our brains to the cloud and hack songwriting right out.
So, in conclusion, if you find after all of this you are still writing songs, making basement tapes, and harmonizing in your head like there's no tomorrow, maybe, just maybe, you can't not write songs.
Welcome to the club.