Sometimes a horse is stuborn because they have been a school horse for many years and just don't like it anymore.Having loads of schooling kids on him day after day might have been too much for him!! How old is he? Squeezing him with your legs might just be what he doesn't like.

I would say try moving him forward with your butt. Try suppling him and relaxing him. work on patterns, What type of riding are you doing? Your teacher should know some things that might help you. Suppling him will help keep him thinking and not let him get bored or want to stop. Also if you can work off some patterns you will keep him interested.
Hope that helps some..