I have encountered this particular phenomenon many a time during the course of my dating experience. The interaction starts of fairly benign, talking about each others' lives, interests, beliefs, experiences, what have you. Then the date planning gets under way, it's about the logistics and sorting out the "what," "where," and "when." Inevitably, there are some hiccups along the way. Either the time(s) I mention I am available don't work, or something comes up before the date.
Then comes the moment of truth; does she make a counteroffer?
Whether or not you think about it, there is subtle communication in this little gesture, or lack thereof. A counteroffer communicates interest, a desire to spend time together -if only to get to know the other person. Lack of a counteroffer communicates -for whatever reason -that she's not very interested in meeting, dating, or spending time together.
It can even communicate that she's actually uninterested in dating altogether -and even impact my interest. I had a first date with a lovely young woman once, and followed it up by asking her out on a second date no less than three times. Invariably, all three times she said she was busy for one reason or another, but she made absolutely no counteroffer on any of these occasions. While it could be perceived as legitimate reasons to have been unavailable, after that many attempts without her showing interest or offering to reschedule, I was done.