I apologize if this gets lengthy; I'm the queen of overly long answers hehe!
I work with a lot of OTTBs, and several of them come off the track with tendencies like that - some cock their heads, some open their mouths, some stick out their tongues, or cross their jaw, etc. What it comes down to is a lack of understanding of the bit.
When they're on the track, the bit acts as little more than a steering aid and a balancing aid. The jockey uses a bridge to balance himself against the neck, and give the horse a stable point so that he won't get too low and fall over himself - basically, the horse can lean on the pressure to keep his balance. It's not used at all like in the English disciplines, in which a rounder, softer carriage is desired. But you also have to look at a racehorse's hind end - because the hind end is the most important part of your headset. A horse can't be "underneath himself" at a gallop in the way that he can at the other three gaits - it's an elongated gait, and the hind end is out behind him, pushing and propelling him forward. It comes under during part of the stride, and the horse compacts. It goes out behind, and the horse's frame lengthens.
Here's the compact, underneath-itself frame:
Versus the long, strung out part of the stride:
See how the horse's body length changes? It's the same principle we use in dressage/hunt-seat/whatever. You want the horse to be compacted.
So, to answer your question (finally, right!?). Your horse is avoiding the bit because he's confused about what you're using it for. He has been trained to lean on it and pull - you won't allow that, so he tilts his head, which is harder for you to get him to stop doing. I think, too, that he may not understand your leg - because, as you can guess, jockeys aren't doing much in the way of leg aids with their knees under their chins!
This is why retraining an OTTB is a gradual process - albeit a rewarding one. The first thing you need to do - and this MUST be tackled first - is teach him, patiently, what the leg means. Walk-work is your friend. He must understand go, first of all. Get him in front of your leg, with a very, very light contact - almost none - and get him trotting out, big. It'll feel fast; let it.
Then he needs to be super aware of moving off the leg. Slowly teach him to yield, left and right, to your legs. Teach him a baby leg-yield at the walk (with a loose rein - it won't be a true leg yield, but it's very effective). Teach him to stop when you sink deep into the saddle and put on a little leg pressure.
This may take days, it may take weeks. Let him tell you how much time he needs - that patience will reward you later when you have a fantastically well-based horse!
Once he "gets" the leg, you can introduce the concept of pressure up front. I like starting OTTBs in a single-joint, medium Dee, and then moving to a double-jointed loose-ring when they understand the bit. A Dee is commonly used in racing, and the familiarity can help ease them into a situation. Work on 'setting' the outside rein, lightly, and using that inside leg that he by now respects so well to puuuush him gently into it. He'll be confused, it's okay. Baby steps are key. Work on this in both directions, giiiiiving and praising if he yields even a little. Don't pull back at all. And remember, pressure should never be continuous. The key to training is not negative reinforcement, it is little gives and releases of external pressure when he's done well. You can work on your baby leg yields with a little contact now, but leg should still be number one. When he is happy with the outside rein, you can play with the inside one, too. By play with, I mean treat it like a sponge. Don't rely on it like soooo many people do. If you're doing it right, you can go through an entire ride with a totally loose inside rein, switching when you change directions. It should only be used as a mild reinforcer, to get that leeetle bit extra bend, and then a GIVE when you get even a bit of yielding. I could preach all day about the power of the give!
All this will eventually lead to a total understanding of what you want, and how to react. It's like teaching a German foreign exchange student English - you wouldn't hand him War and Peace as soon as he steps off the plane, would you?! Your horse needs some 'See Spot Run' right now ;)
But don't worry - TBs are VERY smart, and very quick learners. If you're patient, nailing the basics won't take long. Good luck! :) And if you need me to explain anything, let me know. ;)
^^As a note, lots of OTTB's, and young horses in general, play with the bit as a way to calm themselves down. If he's messing with it/chewing on it a lot, he could be very nervous, or he could be trying to get it out of his mouth....my guy likes to stretch/gape, then pull his tongue back as faaaar as it will go in his head and try to put his tongue over it. He does this with both a regular D-ring (like you have) and the french link snaffle I have now. I'm thinking of going bitless, but I've ridden him in a hackamore before, so I know that he's okay with face pressure.
Vinty is an ottb she will carry her head up and to the outside especially when we trot. But if you have ruled out any pain, we focuse on her body and her head drops right into place you have to work the body and the head will come naturally.
Thanks for the suggestions :) Im really am hopeing that its just something he is going to do in his early stages of retraining, but my trainer have seen him do this and she is very experience with OTTBs, she has retrained many of OTTBs and she hasnt really said anything about it yet, also I think it might be his bit, its a bit I wouldn't want him to have because I wasn't very prepared to get my own horse but when the oppuntuity came to get a horse I took it after wanting a horse since I was 3, so my trainer gathered some old tack and is letting me call it my own until I can get my own, and a new bit is on the top of my list. But I think it might be the bit because after I think about it, when im on the ground leading him and I turn him around he tends to do it to...but idk im just wanting to take care of his headset!
You can't just fix the headset if the bit is pinching or sitting wrong in their mouth. You typically also can't just slap a headset on an OTTB without major balancing and retraining to be a functioning riding horse. A "headset" isn't about the head, it happens when the body is collected and round, and working back to front.
I dunno, I bet we could duel it out and come out pretty even! I usually write freakin novels!
Hahaha, IT'S ON! Someone name a topic; we'll have a Novel-Off!
In all seriousness, though, it's hard to talk about something as important as correct training without writing ten billion words! Training's not simple, so the explanations won't be either.
My OTTB hates fat bits, and went around with his mouth open when I put one in his mouth. He also used to twist his head like you're saying your own horse does.
I think the advice you have been given is great, but I would also get him checked out by a qualified equine massage therapist (sounds fancy and expensive but it's not), even if your horse doesn't look or feel sore, do it anyway. I thought my horse was fine, but I had him checked - turns out he was sore pretty much everywhere, and I'm not just taking her word for it, I saw his reactions, facial expressions and I could even see the muscles twitching and spasming when the massage lady hit a particularly sore spot.
Since my boy's had a couple of massages, combined with sorting out his contact issues the head twisting is virtually gone, and he's a much happier more comfortable horse.