Even Rashi doesn't know
The implication is that telling us that Lavan is the brother of Rivka, a fact we already know, is obvious what it teaches, but that telling us another fact that we already know, contradicts what the obvious implication would be. In my mind, this clears it up.
Why did Yitzchak expect that Lavan would protect Yaakov, and get involved in frateranl broges with the dangerous Esav. Answer: because Yaakov was closest to Rivka and as she favored him, so would Lavan. Whereas Yitzchak favored Esav, and this was further from Lavan in terms of loyalty. This is somewhat confirmed by the next pasuk. "And Esav saw that Yitachak had blessed Yaakov and sent him away (shilach) to Padan Aram. Shalach means to send on a mission to something, whereas shilach means to send him away from here. (This is clear from Rashi's p'shat, that sending him away to escape and sending him to get married, were two different things in Esav's view.) So Esav interpreted the action primarily as Yitchak supporting Yaakov's escape, the rest being a pretense, whereas Yitchak understood it as sending him on a journey to get a wife. So Esav sought to counteract the pretense, rather than to thwart Yaakov's escape, since his father wanted it.
Howeer, in truth, Rivka would have wanted the escape more, so she was relying on Lavan's loyalty to her as her brother. Why then emphasize that Rivka is the mother of both of them? This would inspire Lavan to have the same loyalty to both and not to get involved. Even though Yaakov is mentioned first, nonetheless, this would emphasize that Lavan still would have no reason to completely side with Yaakov. Thus, this pasuk confuses pshat, rather than clarifying it, and we do not know what it meant to teach us.