It could've been a test, or she may have encountered circumstances in your interaction that reminded her of some misgivings/bad juju with a previous man, and felt compelled to address your feelings up front.
Maybe she laughed and had some fun with an AFC who fell in love with her after a date and she felt some regret about LJBFing his a$$. I've sensed this with women before, if you're the first guy she's enjoying hanging out with after a bad LTR ending or something the like, they can suddenly get scared for *seemingly* no reason. Everyone compares women to cats, I think they're alot like horses too.
You were right to push through it and go on unaffected. I'm not saying don't bang her, but play it slow with this one. Life has taught me that's the way to go anyway. Assume she wants you as a FB, but doesn't want you to catch serious feelings and get all puppy dog on her. This happens more often than you'd think.
And if she's worried about you falling in love with her too fast, then for god's sake stay off that phone and NO TEXTING. See her in person as you see fit, but the phone is only for setting up face time. Guys blow it with the stupid text messages all the time.