Let's talk about the psychology of why we don't want or are uncomfortable with singing some of these "uncool" songs.

Some that work with my psyche are these:
1. I want a song I sing to come across as my own, without too great preconceptions on the listener's part--"That's not the way Joe Blow does it," or "That's not the way I learned that, back in the 60s, from PP&M. How can I sing along with you when you don't do the 'standard' version I know?" Frankly, I don't want the listener, Joe Blow, or PP&M singing in the listener's head when I'm singing.

2. The song may seem infantile, or at least juvenile, and thus my presentation dismissed. Various examples might be "Eentsy Weentsy Spider" on the one hand, or some song which was adopted (and sometimes adapted out of recognition) by the writers of grade school song books.
Recently I sang "Drill, Ye Tarriers, Drill", and my wife, a school teacher, dismissed it, saying, "Oh, that's a junior high school song!"

3. Singing such a song as "Eentsy Weentsy Spider" to an adult audience, because it's such a simplistic, babyhood song, is likely to seem a put-down to the adult listener.

I am assuming in the above that the given song was originally, in its own terms, a good song, "cool" enough in its own time and to its intended audience. If it's a lousy song to begin with, the concept of coolitude doesn't even apply, seems to me.

I expect others can track some other mental/emotional reactions that make for discomfort in singing certain songs.

Dave Oesterreich