I was told not to sing at choir in school and generally humiliated about my singing. It made me so miserable that my mother sent me to private singing lessons.
Unfortunately the tutor was very dry, more used to teaching professional singers to expand their range than hopeless children to develop a sense of musicality, so I eventually gave up and decided I just couldn't sing.
Then I met dh, who has perfect pitch. He just would not accept that I couldn't sing, and spent endless hours with me teaching me to sing a scale, to identify notes, etc. etc.
Eventually I learnt to sing just a few songs nicely enough. I won't sing in public, but it made a huge difference to my feeling good about myself.
I am now out of practice though, as children etc have gotten in the way of my singing with dh for the last few years, so I would have to pretty much start over again. I will one day.
The only thing I implore you is not to give up on those who can't sing. Just give them something really, really simple to practice and if they don't get it just keep going. Preferably something they want to sing, too.
Singing is one of those things that people who can do it expect everyone else to do, and feeling unable can be very alienating.