Throughout the serise, even before it become, through the Agni Kai, Zhao clearly disliked Zuko. Why doesn't Zhao like Zuko from the very beginning and didn't respected Zuko.
Although the Zhao and Azula didn't intreact at all in the serise. Would the admiral at least have respect for the princess. Would Zhao be feared by Azula's personality and manipulation. If Century war continued, would Zhao allowed Azula to capture the Avatar? Would he listens and would be afriad of Azula?
Look Zhao's isn't that hard to understand he is just a miserably ruthless and arrogant leader. He's extremely hateful, vengeful and cruel so it should come as a complete surprise that he only cares about himself. For the record I do believe he would have liked Azula better seeing as she gets more praise from the Fire Lord.