If your decision-making has in fact been based solely on merit, this employee needs to understand that favoritism does play a part in the process, but it is different from what she thinks: you favor employees who are productive, energetic, and communicative.
You provided her with feedback on her work, and that is a very important part of this process. If she is truly interested in being promoted, she should also be given specific guidance to increase the likelihood of this actually happening. Obviously, you would make no promises here. Rather, there should be agreed-upon plans for her to improve the way she handles her current work, as well as specific objectives and timetables for supervisory classes and seminars, along with additional projects and responsibilities.
It is not uncommon for employees with questionable performance to make claims about favoritism. You are about to see if she is willing to take the necessary steps to make herself more favorable.
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