OK, I'm a just a guy who's been around for awhile so you can just take this for whatever it's worth. I go by gut feelings a lot of the time, and when I first read this question, my first response is the guy is hiding something. Maybe he's afraid of somebody he knows seeing you two together and doesn't want it getting back to another girl or whatever. Or...
It sounds like the guy may be inexperienced, immature, or all of the above. Look at it this way... do you know or have you ever met his parents? Siblings? Other friends of his? Do some or all of these people also tend to be "no pda" types?
I was a Private Investigator for a little under 20 years. And you could probably call me a professional paranoid. But my BS meter is going off a little. Something isn't right. If you listen to your gut, sit in a quite space (no TV, radio, loud outside noises) and think about this, you might be able to come up with the answer yourself.
There is a really good book you might be interested in buying or renting at the library. It's called "Never Be Lied To Again". Read it, study it, use it every day even just for fun. Eventually, you will learn how to answer these types of questions ever again...
I only have best wishes for you, and hope everything pans out. One last piece of advice for you: Never go into a relationship thinking you can eventually change or fix the other person. You will only make yourself miserable. Go in to any relationship looking for the good, overlook the tolerable, and weigh everything against the bad...
Peace