Everyone's betrayed in The Disreputable History of Frankie Landau-Banks, depending on how you look at it, and it's all thanks to Frankie. While she betrays her friends, boyfriend, and even her father by infiltrating the Loyal Order of the Basset Hounds, it's not as if Frankie hasn't tasted her fair share of betrayal, either. After all, her boyfriend's lying to her face, and the Old Boys' club that is Alabaster keeps trying to squash her spirit at every turn.
Though Frankie betrays Matthew by lying to him about what she's doing (or rather, by omitting the truth), to do any differently would have been a betrayal to herself.
The only reason why Matthew wanted to be with Frankie was because he thought she was pretty and sweet, which ultimately means that he betrays her by rejecting her true self.