Need help with girlfriend

I don't really feel like she is my girlfriend. She said she is, but doesn't really show it. Note: with regards to all the things below, I am not a smotherer. I don't act like a puppy and follow her around all day or text her all the time or touch her all the time. So the problem is not an over-abundance of attention from me. The relationship seems to lack intimacy. She hates PDA, so I understand not wanting to hug/kiss in public, but when we are alone, is it not reasonable to expect a hug or a kiss goodbye/hello? She never wants to initiate a hug or a kiss or a cuddle. When I initiate it, she goes with it, but her not initiating makes me think she goes with it because she feels like she has too. And the whole "initiating" thing doesn't really stop there. Texting; if I don't text first, she will not text me. Going out or hanging out; well, she sometimes asks to do stuff, but 95% of the time it's on me. Sex; she'd just rather lay there without taking any sort of initiative to do stuff to me. But god damn I love this girl. When we hang out and talk it's like I am hanging out and talking with my best friend. I feel like I can talk to her about anything*, I feel happy when she is around and we seem to make each other happy. I know that you must think I am beta loser who has a crush on her but cannot see the obvious signs, but, really, intimacy is only a part of a relationship. What's important to me is that I feel she is a best friend. Sure, intimacy is important, but I cannot allow a part of the relationship to poison the whole thing; I'd rather work on it. I feel like if I can work out the whole intimacy thing, that it would become a fantastic relationship; right now I would say it's good/okay. *But I do need advice on talking about intimacy. I... have never been good with talking about these types of things.

John, I'm sorry this is going on in your relationship. I feel I have this problem too. Sex is very important in a relationship (in my belief) and even the lack of it could end the relationship (it will end mine I'm sure). I know that in my own relationship, my bf complains that I don't initiate either. The only problem is he doesn't sit still long enough for me to initiate. When he does sit for a sec and we start to kiss for a minuet he interrupts and starts talking about what's on tv later, or a issue he had with a family member or he suddenly leaves the room to play video games or he doesn't sit still at all and instead will get up to clean the kitchen or play with the dogs. I'm not the type to just jump up and state "i want sex now". You need to remember that girls initiate sex differently then men do. Its usually slower to start up. And can be signs like her caressing you under your shirt or playing in your hair, pulling her body closer to you in a giving herself to you gesture. This sex issue has led me to not want to text him, or call him, or kiss him when I get home or to go any where with him on outings. I totally agree with your statement "it makes me think she goes with it because she fells like she has too" Have you spoken to her about this? Maybe she doesn't even know how you feel about it. Talking with her is the best place to start. I don't know if this helps you but its a girls perspective any way.