It's hard. Yes, private therapists get to pick and choose. Some like I guess "easy" clients, whatever that actually means to them. Others like "challenging". I would hope that most just base it on rapport and whether they believe they can be effective. If this therapist decides she doesn't want to work with you for whatever reason, look at is as a blessing. Least she won't lead you on to believe she can help if she really cannot. If she does decide to work with you and you still like her, then hopefully it's a good match and you get the help you deserve.