Why does Juliet ask Romeo not to swear by the moon??
According to the words of the play (this is in the balcony scene in Act II, Scene 2), she asks him not to swear by the moon because the moon is not constant enough. It keeps changing from new moon to half moon to full moon and back again. She would rather he swore by something that is a bit more consistent.
O, swear not by the moon, the inconstant moon,
That monthly changes in her circled orb,
Lest that thy love prove likewise variable.
Instead, she asks him to swear by himself because she knows that he himself is constant.
I think you could argue that Shakespeare doesn't want Romeo to swear by the moon because it was a symbol of Romeo's infatuation with Rosaline and would not be appropriate for him to swear by now that he has a warmer love with Juliet.