To be fair, it's less a matter of leadership than a desire to manage her social anxiety. She knows that if she can control the venue and context, she can, to some degree, control the behavior of those around her.
Hence, freewheeling social play at recess is stressful because her friends have total behavioral latitude and abandonment is always a risk... while clubs, classes, formal groups, and games are relaxing because there is heightened context making abandonment unlikely.
That said, she prefers one-on-one socialization to all other options because then she knows for certain that she won't be abandoned.
