But I do think it's clear by the last panel that he's not really firing her, he just lost his temper because his parents' portrait was smushed. It just seems OOC at this point in his Batman career to be all "YOU'RE FIRED!". That's the kind of thing later-Batman would say. (But then again, if Huntress is in town, Babs should be Oracle, so it's all messed up.)