I'll go way out on a limb here and wager a guess....Faile's got jealousy issues?

I think that if you look at everything the Faile does around this time through the lens of potential jealousy, her actions and attitudes make more sense.

As to why she's mad at Perrin, it seems obvious from the later books, that saldean women expect to be handled from a position of relative greater strength.  For Faile, when Perrin yells at Berlain she feels as though Perrin is treating her with respect, in effect treating her as if she is strong enough to handle being yelled at.  (This is a position that seems pretty alien to me I'll admit.)  By yelling at Berlain, but not yelling at her, Perrin is triggering Faile's jealous streak and making her into a pretty intolerable person.