I'm so sorry to hear about your frustration. Sometimes the hardest part is when its in our own nature to open up and talk about everything, but its just not for our partners.
Trust me, I've got two boys who won't offer very much in terms of their feelings or their thoughts on the specifics (though one is better about it than the other). At first I nearly tore my hair out worrying that either A: we'd never be able to communicate sufficiently and it would all just fall apart, or B: I would be the one constantly bringing up the issues, being annoying, and I would ruin any peace between us and it would all just fall apart.
It seems like you're in a similar spot with your man. It took me a little while, but I told myself "Ok. Its my personality to bring things up. Its NOT in his personality (or the other one's) to just offer up what's on his mind. That's just the way things are, and that's ok. Now we have to come to a compromise for this to work."
Being the way your man is, you could ask him to promise that no matter what he will open up and tell you anytime the littlest thing is bugging him, or even ask him to promise to tell you when there's something big on his mind. And he might even agree to! The problem is that he may not even be thinking about those things. They may float into his mind, and his way of coping is just to push it aside. So if he doesn't even consult HIMSELF on the issues, why would he bring them up to you?
Your Needs V.S. His Needs
The only answer here is compromise I think. Tell him that to be happy in this relationship, you really REALLY need to discuss your feelings, and get feedback about his. Emphasize that it is important to YOUR happiness. At this point, refrain from any accusatory phrases like "You don't talk to me enough!", instead you could say "I need more discussion, and I need your help to do that."
Tell him that you realize its not like him to just start talking about it the way you do. Say that you are more than willing to be the one to bring up these conversations, if he's not sure how or not sure when, but tell him that you're worried you will come off as being nagging. Reassure him that you don't want to annoy the shit out of him, but that there needs to be a middle ground also. Not talking annoys the crap out of you, nagging him all the time frustrates him. Tell him you realize this, and so you want to agree to meet in the middle.
What he might promise to do for you:
Ask him to please keep his cool and react with a level head when you bring up sharing feelings. Scowling at you, or rolling his eyes, or not looking at you are harmful behaviors that make you feel like you're not being listened to. So if he does these, tell him to please refrain. Instead, if he does feels these responses creeping in or he can't help it, tell him that he NEEDS to instead say, "Honey, its important to me that I understand your feelings. I just can't talk about it right this very second because I can't have a conversation like this without reacting emotionally."
Assure him that its ok for him to say "I can't talk right now", and ask him to try finishing that phrase every time he says it with WHY he can't talk right now, so you just don't feel like you're being ignored for no reason. "I can't talk right now, because I've had a really stressful day and I'll probably just get defensive too fast".
What he can expect from you:
(and leave room for him asking for his own specific needs)
Now you need to put in the work and have the emotional intelligence to know when its a good time to bring things up, and when its not. I'm sure you've had those moments where you really really really really wanna talk about something, but its pretty obvious he's feeling like crap and saying anything will just make it worse. Holding it in makes you feel terrible though. When this happens, I suggest approaching him in a relaxed manner (maybe throwing your arms around him and planting a kiss on his forehead) and saying something like "I know you're feeling well. I have a lot on my mind too right now, and I really need to talk about what I'm feeling soon. I know now's not a good time. Let's talk about it when you're feeling better instead of now, ok?"
This shows him that you're capable of understanding his needs, and helps him know you're not automatically gonna nag him all the time. It also gives you a way to let him know you've got lots of feelings rolling around in your head so that he can appreciate your restraint in lieu of his needs right then.
Tell him that you will do this for him. That its not all just asking him to make promises to you, that you're working really hard to make sure you're both happy with this. That this is for your happiness as much as it is for his, and you'll work on it for him.
The really tricky part:
What if he just uses the "I can't talk right now because X" phrase every time you want to talk to him? Well, by design, he's allowed to do this. You said it was ok for him to say it, and it should be. The problem is that at some point it becomes unfair. You're not meeting each other half way if he's the one always backing out, and you're the one always holding things in. If this does happen, you need to sit down with him and explain calmly that you feel like your patience is being taken advantage of. That maybe he's got valid reasons for not being ready to talk, but in the meantime, its making you really unhappy. And all the frustration HE would feel as a result of talking, is what YOU'RE now feeling as a result of NOT talking.
If you guys can't come to firmer ground after that kind of talk, then maybe its time to think about how happy you two can really be together as a functioning couple. Consider that it might make the both of you happier people to change the relationship. Its a scary thought, but in the end if you can't find middle ground, neither of you will be happy together and it might be better to move on.
Man... listen to me go on. That's what you get for encouraging me. I hope this helps though. I honestly know how you feel, and this has worked for me. Maybe it can help you too.