Am I overreacting to children's bickering? IIN?

You are right, my son is extremely strong willed! In general, I'm not terribly concerned that this girl would talk him into doing something he knew was wrong (the possibility that he might convince her to do something unacceptable is probably actually greater-- she seems very immature for thirteen).

But I don't think it is particularly healthy for a nine-year-old to be put in a position to essentially be the one to "look after" a thirteen-year-old. There is also the matter of her generally negative outlook on life, rudeness, and the tall tales she constantly tells.

After posting about this, I've had some heart-to-heart talks with my son, and he seems to be of the opinion that, while he doesn't want to be "mean" to the girl, he doesn't want to play with her or hang out with her, either. So, we are working on strategies to be kind, while not engaging the girl.

And yes, who knows, perhaps in time she will mature a bit, and the two of them can have a more positive friendship in later years. Thank you for your heartfelt responses.