Communication is key. He may have been "processing" or just pissed for the moment and afraid he might say something he couldn't take back. That is a point to remember. Words said in haste can't really be taken back, you can apologize and say you didn't mean them but they are already out there and they will forever be in memory. I think you seem to be handling things well.

Good for you for wanting to make this relationship a healthy one. I recommend having a "guide" to help both of you to learn how to do that since neither of you have a model on how. This could be a relationship counselor/therapist or a class or a book you read together.
My gf and I just read Harville Hendrix's book, Keeping The Love You Find. John Gottman is the Godfather of relationships. Guy and Kathryn Hendricks have good books as well.

Disagreements are bound to happen in any long term relationships. What matters isn't that you never argue, it's how you deal with them and it's being as honest as possible with each other. In time you will understand each other's mood better. Perhaps, instead of snapping, next time you sense him being distant you could simply ask what he's upset about. 9 times out of 10, you'll find out he's preoccupied with something that has nothing to do with you, or he's simply tired.