I just typed out a long answer and lost it in trying to post.
instead, let me ask what kind of bit this horse is using. and, does he do this for everyone who rides him?
what I had typed, and I guess I can type it again, is that if you pull too hard toward one side, let's say to the right, the left rein will actually start to engage the left side of his mouth, saying , in effect, 'turn left' , while the right rein is really saying nothing, or "turn right".
neck reining is more about LIFTING your rein, and laying it on the outside of the horse's neck, rather than pulling the horse over to one side. if the hrose is not following the rein with a lift and a bit of outside rein on the neck, then they are doing so because either they are not well trained, or you are being too hard/fast, or they have a different place they want to go, and they know they don't have to follow your direction. they can sus us out so fast, it's crazy!
as a learner, a novice, I'd have you in a snaffle and direct reining first. and learning to get that horse to pay attention and obey you. that's why I am asking what sort of bit he is wearing.