I didnt say hate.
Luffy beating Kat, putting aside the personal challenge of wanting to surpass him, was motivated by the fact that Katakuri was the main challenge for the Strawhats to escape, Luffy does not beat him, the Strawhats ain´t getting away.
It´s the same as Luffy targeting Lucci from the get-go because he knew if he does not stop him, Lucci will go after every crewmember, which is articulated several times.
So it´s not hatred, it´s the stakes and context of sheer survival, and mostly not your own but the crew or people you hold dear.
Sure Zoro welcomed the fight vs Ryuuma to a certain extent, but the main reason behind the fight was Moria army + Brook´s shadow.
Kaku and Zoro respected each other in their fight, does not change the fact that Oda has always emphasized the crew´s role in the Strawhats´ fights, in particular to Zoro (vs Mr1 he thought of the crew while near death, vs Ohm Chopper´s condition, vs Kaku the key situation and Kaku insulting Robin....)
Of course Oda can change that (or like nik said introduce some kind of connection between Mihawk and WG), neither have examples in the manga up to now though.