Because Perrin would not be able to understand why she killed someone who needed killing. He doesn't understand the idea that someone can be so crazy and dangerous that they might turn at any point, and he prefers to wait until a danger has become clear and present to act after years of slow, ponderous though. Faile, on the other hand, is not willing to take that chance, so she came to a decision, acted on it, and then modified her response based on her understanding of Perrin as a person.

That is one of my favorite scenes, actually, and I hope Elayne, Aviendha or Min get the chance to get rid of Mazrim Taim, because his danger is obvious to everyone but Rand.