So many people think that the reason Katakuri respects Luffy is because he was the first person (maybe in a long time) that gave him SO MUCH trouble, such as almost making him lie on his back in a fight, constantly dodging some shots, and even exposing his donut ritual to some people. I disagree.
Evidentially, his age is currently 48, more than twice as much as Luffy. He was already more than Luffy’s age when Gol D. Roger conquered the Grand Line and got his Pirate King moniker. This means he might have already been a great force to be reckoned with in the Big Mom Pirates crew fighting the other Yonkos in the seas. And he can only grow stronger than that. The people he fought were presumably not easy.
Another is that we have already heard from Rayleigh that battling beyond your limits improves your haki tremendously, and right now, he has by far the strongest showing of Observation Haki in terms of precognition we have seen without ambiguity. You do not grow your haki THAT strong if you haven’t had your fair share of life-threatening bouts. Although, we can argue that each person has their inclinations towards things (e.g. Zoro on Armament Haki, Sanji on Observation Haki, Luffy on Conqueror’s Haki) and may give idea on the potential of the user (possibly very great for Katakuri), it still requires the process of getting into that state. So, again, not had it easy.
Lastly, he has Observation Haki, and he CAN control it, as was seen in their Conqueror’s Haki clash. This is by no means, again, easy.
Now, why did Katakuri started respecting Luffy if not for his strength? The simplest answer is his CHARISMATIC TENACITY. You can see Katakuri somehow appreciative by this willful (haki-full) person standing up to his beat-down many times in the fight, showing the tenacity of a king with great ambition. Him having Conqueror’s Haki may also give credence to how he might have empathized with such willfulness, maybe even to the point of seeing a bit of himself and his own willfulness and tenacity in Luffy. And Luffy, having probably felt Katakuri’s appreciative emotions (he was sensitive to emotions), responded accordingly to have this manly fight leading to his eventual turn-around of a character, of course lending to Luffy’s charisma.
Tl;dr Luffy did not give Katakuri his so-called “fight of his life”. He, however, was enthralled by Luffy’s charismatic tenacity, and thus came to respect him.
*Theory by Tinduz
