When my daughter, Amy, was in the fifth grade, she qualified as a GT student. My wife and I sat down with her, explained the short list of pros and cons, and allowed her to make the decision. She told us exactly what your daughter told you: Her friends were not in the program; therefore, she didn't want to be there either. The school was disappointed, but they got over it, and Amy went on to be an honors student at the University of North Carolina.
I speculate that your daughter doesn't want the attention that would come from being pulled out of class by the GT teacher. She is concerned that her “special” status might not sit well with her friends. Unfortunately, her anxiety is probably warranted. Since the efficacy of such programs has not been demonstrated, since they are obviously not necessary to a successful life, however one might measure that, I'd say let your daughter make the decision.
“But what if she later regrets it?”
Good. Then she has to deal with the issue of personal responsibility, and she is not too young to have to do so. It is controlled exercises in decision-making of exactly this sort that cause children to become more far-sighted and weigh pros and cons rather than simply making decisions on the basis of feelings and impulses.
Regardless of outcome, being allowed to make decisions and learn from the mistakes that are inevitable to that process is an important part of growing up. In the emotional sense, it is the very thing of growing up.
Family psychologist John Rosemond answers parents’ questions at www.rosemond.com.