+1 - what he said. Playing with or in front of other people at every opportunity is not only an important part of developing as a musician, but also builds capabilities that help in many other aspects of life. Learning to feel comfortable and enjoying working with a crowd will stand you in good stead whatever career choices you make.
On the same track - learning to breath effectively will also help you when speaking.
Apropos your original post, I suspect that your teacher is on the right track and there's just a gap in the way he's communicating with you, your listening to him and/or both. Problems with not being able to play your best in front of your teacher most likely boil down to not having put in enough hours to habituate what you do when practicing alone (JMHO).