There's a difference between wanting to carry his head low and pig-rooting.
If he puts his head low quietly, carries it confidently there, and still remains responsive, then it's likely he was trained that way to begin with.
If he pushes his head down forcefully, pulling you off balance and/or the reins through your hands, and then puts his head back up to normal, then he's pig-rooting and that's unacceptable behavior. He doing it intentionally to get out of listening to you.
I'm not really sure of these is occurring, so I don't have any advice to give at present.
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