It's often the case with gifted children that they..well they don't struggle emotionally - they're just emotionally different. Often they feel ostracised at school because they're simply not thinking in the same way as the other kids. This is perfectly normal (we come across it all the time!), but it can mean that they're not all that keen to put up their hand in class.
I think school is really important for developing their social schools, but it should not hold them back. As Mark Twain said: 'I never let my schooling get in the way of my education'.
There are many options open to you, from home schooling, distance learning, to specialised gifted groups and programs.
All the best.