It is around that age where teachers start teaching the "correct" way to hold a crayon / pencil, so it could be that she embarressed him in some way when correcting him.
One of the other children might have teased him if he continually goes over the lines and if he is a sensitive child, it could also be affecting him.
I have found with my 2 boys that I need to help / correct them in very different ways, so I can imagine a class with 10+ children it can be difficult to figure out how best to treat the individual child.
But I agree try speaking to him about it. I know you said he does not want to colour at home anymore either, but maybe if you colour with him, even if he just sits there and watches, you comment on how much fun it is and how much you are enjoying it etc, he might become curious and try it out himself again
Then schedule an appointment with the teacher and discuss when it started (something might have happened in his life that seemed small to you, but huge to him - at home or at school), was there any bullying happening at school, was she correcting his grip / encouraging him to draw within the lines, is there any way he could think that his classmates were laughing at him
Then also discuss a constructive way of coaxing him back into drawing, cos yes, it can affect future pen control, hand writing etc