Do women sometimes test men or play games with us when it comes to texting and telephone calls?

Alright! Been out on about 6 wonderful dates with this woman! But sometimes when I text her, she sometimes replies back real quik, and sometimes it may take her a day or so.. When it does take her a day or so to respond back to me, she will text me back talkin about she forgot to respond! What the hell!? I don't text or call her alot anyway, because I don't want to bug her! When I do call her, she doesn't answer her phone! She may call back after I made 2 attemps to call.. She did tell me that she doesn't like to talk on the phone, but damn! Although we have been on 6 dates, she doesn't consider us dating seriously yet! And what really confuses me! she told me that she is still open to date other people, but I'm wondering what does our dates mean when I'm holding and kissing her!? I really want to be with this woman! I don't know if she is trying to play hard to get or what! Should I step up and be more persistent? Or should I go with my instincts and back off?