After watching
episode 13, I might missed something...
We agree that Kaname likes Yuuki (as a lover or for hidden motives is not clear).
So, he wants to be with her.
Also, we agree that Yuuki cares for Zero (as a sibling, friend or lover is not decided).
So... why did Kaname help his rival Zero?
If the answer is in manga or in next season, then please don't tell me.
*points to her sig*