I think more that they are embarrassed of themselves. They have so much fear from with in that they do not see how they are affecting those around them. They only know how they feel on the inside and don't really care about anyone else. They want to follow "society's rules" by what they have set for themselves, but don't realize that rules are meant to be broken some times.
They feel that they must please those that are like them so that they may become a part or stay a part of their group. Its more often than not that they fear those that they are trying so desperately trying to impress. Its a defense mechanism inside of them that fears change, hope, love, and other things. They don't know any other way.
If you want this person to be open about your friendship or relationship you have to show them that they have nothing to fear. You have to show them that they are worthy of anyone's love/friendship and that they have yours. You have to help them see that they are only damaging themselves by being so closed. You may even have to show them that you are willing to fight for them and that they need to fight for themselves. They more than likely don't feel like an individual, but an outline of their other friends.
You also need to make sure this person is worth it, to be perfectly honest. You need to make sure that they are the one that is worthy of you. If you find that they are, then do what is necessary to take care of them and help them understand how you feel about the situation. Because in some cases they may not even realize that they are doing it. Its something that you must make them aware of, and how it makes you feel.