i guess this is what they call a fighter's spirit :3 for ayano she had to prove herself by defeating catherine but as we can see she isnt a melee type fighter like ayano being more of a "spellcaster" type controling familiars and such ~ i would say that there wouldnt have been a point to the match if she aimed for Catherine and not the familiar given that this would be considered "cheating" in a way ~ and of im sure she would be smart enough to have her familiar defend herself if attacked so maybe ayano didnt see any point in aiming for her at all ~ besides beating the familiar does mean that Catherine loses and its not like she is offering any support to metatron...
and its a given rule to use your trump card last in defense for her lateness in using the "purification flame"