Howard,

"Unless you suffer from some neurological disorder you should be perfectly capable of remembering vast amounts of information."
This is true. But having something stored in your memory does not guarantee it will be immediately retrievable when you need it.   It is not that uncommon for someone to "blank out" on the lyrics of a song that they've not only learned and overlearned but may have performed before audiences many, many times.
Perfection is not guaranteed, no matter how long you've taken to memorize something.   Most artists use song sheets or the like in the recording studio; not having to be searching their memory for the next line frees up your attention to focus on things like your interpretation, sound, etc.

I can see practicing a song 100 times in private before you perform it in concert, but before you share it with a few friends at a small, informal song circle? Why??

The hardest lyrics for me to recall perfectly are often my own songs. That's because I've often revised some of them a number of times before arriving at my (currently) final version, so there's a lot of interference.   And if I want others to sing along with me, it's almost guaranteed that they won't be able to if I don't pass out lyric sheets (or even sheet music, if the tune or harmony is unusual).

"Someone said an amateur practices until he gets it right, a professional practices until he can't get it wrong."
Whoever said that is wrong.   There are few, if any, professionals who never make mistakes — whether they are doctors, teachers, mechanics, journalists, or musicians.