She ignores me when I ask her out, yet keeps talking to me?

Anonymous
So I started dating this girl a couple of weeks ago. We had a couple of great dates, I was really into her and it seemed like she was really into me (in fact, she said she was). Anyway, then she canceled a date last week because she said she was sick, yet kept talking to me and we made plans for the weekend. She would text me in the morning and she called me on friday, in addition to gchat and stuff. Then Friday evening she canceled, saying she forgot that she had to host a prospective student for her program that weekend. When I suggested hanging out next(now this) week, she said she'd let me know as soon as she knew she was free. Also, she apologized several times and said things like, "do you hate me?" and "please don't be mad."

So we talked sporadically, and on Monday I texted her asking her how her day was and if she wanted to hang out this week. She responded to the day question but not the hanging out question. So I decided to leave it and let her come to me. She initiated a gchat with me yesterday, and was very conversational. After about an hour I said I had to go, and casually said something about how I knew she was busy, but that I still would like to get together at some point and she should let me know. She instantly signed off after that (usually would say goodbye). So I figured that was it, but then she gchatted me again today, and acted like nothing had happened! This time I didn't ask her about getting together, and she didn't bring it up.

So my question is, does anyone have any thoughts about what may be going on with her? She seemed really interested, canceled twice last week, said she wanted to reschedule, kept calling/texting/gchatting, but she ignores me when I ask her if she wants to hang out. If she is not intereted, then why would she keep talking to me? I am not initiating anymore at all, so I don't see why she would just be doing it to be nice. That would make no sense.
She ignores me when I ask her out, yet keeps talking to me?
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