I ride a horse which used to do the same. It didn't matter how small the fence were, it did it even when there wasn't fences at all. I hated jumping with it, because he jumped often too far and pulled his head down after the fence. Then I got a new instructor, who immediately told me that I need to collect the horse, to think that it will canter more up than forward, and really collect it. And that really did the trick! Now I can always bring it to the right place where to jump, and it really jumps nicely, softly and without pulling his head down.
When you want to collect your horse (I don't even know if the collect is the right word, English is not my native language), you need to use your legs. The more you use your legs, the more horse uses his (back)legs, and then you can ask it to raise its head. If it doesn't move enough forward, you just can't use your reins to pull his head up or the horse will stop or try to resist, it might not even jump after a while if the riders always pull his mouth.
You'll never get to heaven if you're scared of getting high