Falling for someone who doesn't seem to want to catch me.

Hi. I'm a third year graphics design student originally from the UK but moved to SA when I was around 18. Anyway, for the past three and a half months I have been dating this girl- oh yea I'm a lesbian btw. She's amazing really funny smart a psychology student. We are exact opposites apart from her being black and me Caucasian. I come from a very loving open minded family- they all know I'm a lesbian- while her family-from the small hints she gives off- are very mean and homophobic. I have a strong suspicion that she was abused emotionally and physically while growing up because she says things like ' My dad yells at me whenever I cry or show any emotion and tells me it's my fault', also the scar on her arm she won't tell me how she got. I am open with her about everything without her asking but with her it's like pulling teeth. I love her so much but it's really annoying how she won't open up to me. How do I get her too? P.S she's scared to come out because of her family.