I don't know much about your art, but this seems extreme to me. If I can modify it to apply to what I know, it sounds like your situation would be simlar to a student who wasn't good at a jumping technique (because of whatever physical weaknesses) but still followed along in class and did his best. But then to have the instructor tell that student he must demonstrate his jumping skills (or lack there of) to the entire class as they all stood around and just watched many times over seems pretty harsh. I guess I just don't understand...
I'm not sure I understand what you are saying exactly, so I'll try to paint the picture a bit more clearly.
When we train the physical side of capoeira, then that is what we focus on. The musical side comes into the picture when training is done, and we play in the roda. This is where we actually "DO" capoeira, as opposed to practicing the technical side of the art. Capoeira can be sort of a playful fight (altho it can be brutal, depending on the personalities playing together). The art uses a rhythmic music to set the pace and determine the type of play (sort of our version of sparring). This comes from the Afro-Brazilian slave roots of the art, wherein the musical culture found a place in the fighting art.
The songs that are sung usually relate some history of the art, wisdom from old masters, or can be playful ribbing at classmates and whatnot, and the one's who are really good can make up songs on the spot to make fun of somebody if they do something silly or foolish in the game.
It is during the play when the music drives the game, that the observers will sing while waiting for a turn to play. This is when it is expected that everyone (hopefully) will contribute to the singing. But usually nobody is actually put on the spot in front of the crowd to sing, altho sometimes that can happen during a training session to encourage people to learn the songs. Sometimes, if only a few people are taking a turn at leading a song, the teacher will say something like "you can only get in to play if you sing a song first". That's when we can see who is really uncomfortable with singing, because suddenly participation in the roda drops to a select few who are comfortable with the singing.
I have actually made some effort to sing. I do my best to sing the refrain, but I don't like to lead. I have made the effort to learn a few songs in the past, but it is just rote memorization for me, I don't understand what I am saying, and I am sure my pronounciation is terrible. I find that Portuguese is a very difficult language for my tongue to make, and for my ear to hear. I have even taken some turns in leading a song, but I really dislike it and it generally doesn't come out well for me, altho the group is actually pretty supportive of getting people to sing and nobody is expected to sing like an angel. Many of the songs are pretty simple and rough anyway, not something for the opera. Just singing at all contributes to the energy and is appreciated all around.
So at any rate, it's not like getting up in front of a crowd to sing a recital. It's within the context of the play, and it's very fluid and changing, songs weave in and out as the games are played and people take a turn and then it's carried on by others and never really stops.
I just don't like singing, I never have, I don't like to express myself that way, and I don't like to be the center of attention. I'd much rather fade into the crowd that way, I can sort of follow with the chorus, but that's the extent of my committment to the songs. It made me uncomfortable for a long time, but I finally just sort of made peace with it for myself and said, well, that's just me. Maybe I'm selfish, maybe I'm myopic about it, whatever, but that's my position with it and I don't let it bother me anymore.
If you see some examples, it might help you understand it better. Check out this link, this is the website of the school I trained with and they have some video clips at this site. These were taken long after I faded away from the group, but there are some good examples of different types of games, some fast and furious, others more controlled like a chess game, but all have the musical side presented as well.
http://www.abada.org/gallery3.html