Can someone be a real friend if they're top secret about everything but want to know everything about you?

I was very close to this girl I met at work for 8 years. I was very open with her, she met my family, even became part of my family. The thing is, she was over the top secretive about everything. Didn't want me to know her age, about her family, her lovers, where she lived, etc. If I casually, politely brought it up, it upset her. I put up with this because I thought if I'm open and vulnerable with her, eventually she'd come around and be the same with me. It never happened. I got frustrated and politely distanced myself. Then I felt kind of bad because she was actually a good friend inspite of everything. But I couldn't take the one-sided thing. So I tried reaching out to her and reconnecting, and she just wasn't interested. Eventually, I just let her be. She even removed me from her Facebook. Then months later she hangs out with my brother that she knows I've had problems with. She would actually sit and talk to me about how awful my brother is. Isn't that the most garbage, 2-faced person ever?
Yes, she's a terrible person.
No, she's not terrible.
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Can someone be a real friend if they're top secret about everything but want to know everything about you?
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