There was a question on a blog about whether people have had students cry in lessons.
I can't remember if I ever cried in a lesson; I don't like to cry in front of people. I did almost have a panic attack in a piano lesson when my teacher tried to get me to sing. I now realize that's a necessary skill, but I was in high school and super self-conscious, so she let me get away with humming.
As a teacher, I've had plenty of children cry in their lessons. It's usually due to frustration, and I admit that I sometimes push too hard and/or miss the child's cues that they're at the crying point. If it's a total meltdown, I utter a silent prayer of praise that the parent is in the room and I calmly end the lesson. If it's just regular tears, I let the child decide how to proceed. I never jump in to comfort beyond mild verbal reassurance, because that's not my role.
I actually prefer tears to the little guy I had once who just shut down every single time I asked him to change or repeat anything. I was reassured to find he did this with two other teachers before me; I hope he's finding life easier now than he was then.