Well, just like if you drive a car, YOU are responsible for keeping it on the road. So, therefore, you (as the rider) as responsible for where your horse goes.
If the horse is not doing what you are asking, then are you likely NOT asking for the correct thing OR your horse does not understand what you are asking. (Which would be like hitting and brake and the gas pedal at the same time in your car)
Are you riding Western or English? I'm just curious if your riding instructor is having you ride with one hand or two hands on the reins.
For an issue like what you are having, it would likely be easier for you to have two hands on the reins. Let's say you are going around the arena to the right, in a clockwise direction. That would mean your left hand is along the wall (outside hand) and your right hand is your inside hand. So if your horse is wanting to go right and go to the middle. Then you would use your right LEG (inside leg) to "block" your horse from going that way. Make sure your left (outside) leg is not making contact with the horse so that you "open the door" for the horse to go that way. With your reins, you would use your left (outside) hand in a direct rein fashion to steer your horse back to the left. You would still keep a little contact with your right hand (inside) just to be there to balance and support the horse.
If you are having trouble understanding this or knowing what to do, ask your instructor!!!
