We hear on our riding lessons push the horse into the contact or push the horse more forward. Unfortunately most riders react by leaning back and shoving with their seats very heavily into the horse's back.
Now imagine someone was trying to push you backwards ,and you did not want to fall back. What would you do?You would use your core and thigh muscles to resist against them. You definitely would not lean back and tuck under with your seat .
So the next time your instructor says push the more forward, try to engage your core,stay more upright ,and you will get a much better reaction from your horse.