I'm going to point out my classmate's grammatical errors
Your classmate might be upset with you for doing that don't you think?
Yes, I think I can help with his education.
It's good that you want to help your classmate improve. Just make sure that you encourage him when pointing out the errors.
I'm going to humiliate him by pointing out his errors, it'll make him feel like it's all his fault and fix his problem.
That seems rather harsh don't you think? If someone did that to you I think you would feel embarrassed and hurt. Try to help him improve and encourage him to do better. Humiliating someone won't make you feel good about yourself.