Why is my boyfriend hiding our relationship

Help! Why is he hiding me?

Hello my dears,
I'm slowly despairing, so I urgently need some advice from you.
I (24) have been together with my boyfriend (29) for half a year now. But it is slowly getting to me that he is hiding me. Specifically, this means that when we're in public, we don't appear as a couple, if I take his hand, he has to scratch his nose or something and then doesn't give me his hand back. Except for his best friend, I don't know anyone in his environment, although he probably meets up with friends or family once a week. For example, if I'm with him and his parents announce themselves, he even throws me out of the apartment. However, he already knows my family and friends. Besides, he never talks about future plans or anything. That actually strongly suggests that I'm just some kind of affair. But what speaks against it is the following: He came to my parents voluntarily and since he has known my girlfriend, he has regularly invited her to evenings together and lovingly takes care of both of us. Every 2 months he travels for a week on business, but then calls me several times a day at the international rate, sends me pictures via Whatsapp, and even brings me relatively expensive gifts and gives me a concert ticket for January 2016 for my birthday (the other card he owns). Even during sex, my orgasm is much more important to him than his own, so I really can't believe he's just playing with me.
By the way, I also find it funny that he hides me from his surroundings, but doesn't put all my things away in the bathroom, which visitors can tell without a doubt that he has a girlfriend. If I ask him if I could get to know his parents, for example, there are only strange excuses.
What are the reasons for his behavior and do you have any tips on what I can do?
You would help me a lot.