I find that often horses are trying to tell you something, maybe the might find this method irritating and he's trying to escape the half halts? Try to see if you can get him round from and steady contact (like pressure and release) as he will then seek the contact from your hands rather than try to escape it by pulling. Don't forget also it's hard work for a horse to use its back end and work in a frame so give him a walk and let him stretch his neck and muscles out, and then try again
My horse does that when hes being asked to work from his hind end and trys to evade the work. If you roll your shoulders back and pinch your shoulder blades together so when he pulls down and out he hits a wall of sorts and after a few tries he should stop or at least not do it as often.
If you constantly half hault your horse will grow immune to it. And won't notice your command if you constantly use it. Used learn by pressure release. Apply your pressure when he gives you the correct answer release. Half haults don't work with every horse. So keep your pressure in your hands while pushing him foreword with your calf. He might just need more pressure release than just a constant half haunting que your whole ride.
Try to gain connection in different ways- for example, lightly hold the inside rein and bump the outside one until your horse gives. Often people "overuse" a cue, so the horse eventually ignores it.
Also try not using so much leg. Putting leg on while putting pressure on the bit can sometimes confuse the horse and that can cause head tossing or them pulling the reins away. Another thing is look at the type of bit your using. He may need something softer or a different type of mouth piece. I know for my horse he uses a myler level one mouth piece because he is so sensitive. Some horses are ok with single jointed and some aren't.
You can try lightly squeezing your ring fingers one at a time rotating which one your squeezing(left,right,left,right) almost like a light half halt with one finger. This will keep the reins a little more quiet while still sending the correct signals to your horse.