My thoughts are below. Take what is helpful and disregard the rest.
Do I walk away or continue to fight for him??
Sometimes walking away is letting someone have the space to work on themselves. He has been telling you for a long time by his behavior that he is not ready to be in a relationship with you. Quite clearly.
And why do I still care for him?? Why is my heart feeling broken when I know it shouldn't - not with what I put with!
You are a feeling human being, and that's ok. Love can be real - and love alone isn't enough to make a relationship work. It's totally ok to care about him. You are a person of great compassion and that is a darn good thing. This world needs more people who give a damn.
It does seem like his choice to do the hike is leading down a path of self destruction - it may bring temporary peace but I know the issues will remain until he deals with them.
You can know that he needs to deal with his stuff, but that doesn't make him ready to do that work. And it's heavy work. You describe "forcing" him to get help. What you are experiencing now is the reality that someone can't be forced to deal with trauma. They have to do it when they are ready.
I don't see any problem with wanting to do a hike designed for veterans. Those leading the hike probably know vets are trying to run from their stuff, and generally are there to try and help. His trying to escape his pain by connecting with support designed for veterans actually seems like a healthy option. He's running to connection and support. It may not be your support (which I know is super painful to accept) but at least he's going towards support for veterans. Quitting treatment wasn't wise, but treatment through the VA isn't enough for many (most?) veterans who are really struggling. Sitting in a room talking through the VERY worst of what can happen in this world isn't something everyone is ready or able to do. (I am not a vet, but I couldn't do it for PTSD myself for a long time.)
If he joined the same 6 month Appalachian trail hike for veterans that was recently reported on by NPR, Warrior Expeditions, damn, it seems like a great option. The whole point of hikes through that nonprofit is to help veterans work through their stuff. It may not be what you would do, but as you said, he's an adult. He's likely had feedback from you and his therapist, and it's good for him to make the choice to engage support, and which support he is ready to do.
I guess my question at this point is how do I move past all this?
Breakups are hard to face in the best of circumstances. It's going to be painful for a bit. Grief is part of the process. Connect with your own supports and friends as much as you can.
he stopped counseling because his counselor got in touch because she was concerned that he just discontinued care so abruptly...
It's probably time to step out of his care. Continuing to be a point of contact for his therapist will just bring you back into it again and again. He's got a treatment team there at the VA for him when he is ready, he's got options for other support. Now it's up to him.
Don't keep contacting him. Everything he is doing is telling you to give him space. Don't keep initiating texts or calls. Let him seek out other supports instead of contact with you. In time, it will get easier for you both to move on. It might also be worthwhile to work on what lessons you can learn from this experience and relationship. This isn't to state that anything he did was your fault. Nope. Not at all. He is responsible for himself, and you are responsible for you. You jumped in and have tried to do so much to change him. It might be a good opportunity, as you described, to take time and space to work on healing for yourself. Learning how to set boundaries (which isn't about changing or controlling others but ourselves and our own lives) might be a good skill to work on for future relationships.
I hope that the pain of letting him go gets easier soon. :hug: