She rejected me but acts like she likes me, should I give up on her?

metroknox21
I met this girl at college a few months ago. I got her number and after a few weeks of texting each other, we became kind of close. We would talk on the phone for 2-3 hours at times, we would also occasionally go grab something to eat after class. I finally got the courage to tell her my feelings for her. She said that I would make a great boyfriend, but that she doesn't think that she is the right girl for me. She is very religious (Christian), I am not. I was disappointed but decided to be her friend any way.

She said that was going to try to be less flirty, but she hasn't. The day after I told her that I liked her, she wanted to hang out, but I was busy, and she sent me a text saying: "Are you playing hard to get now? lol". I played along and joked back saying "you had your chance, you can't have me now". We continued hanging out, texting and calling each other like we normally did. She has told her friends about me, and she wants me to tell my friends about her (I haven't, she really wants me to, I don't know why). Before the semester ended i got a text from her saying: "I wanted to know if you wanted to lay on the grass with me". It kind of upsets me because its messing with my feelings.

The semester is now over. I got a text from her about a week later saying "I sorta kinda miss you", But she didn't want to hang out.

A few days later, she saw met talking to another girl. She texted me the next day wanting to hang out. We spent 5 hours together that day, it felt very much like a date. During this "date", she said that she was sad that friends were in relationships and that she was single.

Does she like me, or is she just messing with me?

Everyone tells me that once a girl rejects you that she's not going to change her mind. So I'm thinking about just moving on.

Also, she is a very friendly person. She has a lot of guy friends that I have met, but she says that they are not really friends, just people that she has met.
She rejected me but acts like she likes me, should I give up on her?
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