Take your pick, I've come up with several ways to explain the "Cassandra Cain will no longer be a member of the Bat-Family" line we got.
"Cassandra Cain will be Batgirl... but against Batman's orders! She's Batgirl, but not part of the Bat Family!"
"Cassandra Cain will be Batgirl... and so will Babs Gordan! Two people sharing the role, with Cassandra in the action, and Babs providing support from affar. Cassandra's not a member of the Bat-family, because she's REALLY part of the BATGIRL family!"
or
"Cassandra Cain is not a member of the Bat-family. Cassandra WAYNE is!"