@.access:
It's not a selfish fight, it's not being short-sighted. He knows very well this may be his last chance to improve before fighting Kaido and it was made very clear to him he is in no condition to face a Yonkou. He may help his crew now and skip this fight with Katakuri, but only for all of them to be destroyed by Kaido a few days from now, or he can believe in them to run away and use this opportunity to improve himself and maybe have a chance to keep his crew alive once they go to Wano.
It's still a selfish fight. It's the same thing when he punched big mom and got Sanji captured at the tea party escape. He just doesn't want to admit he's lost and it's his pride he's putting over the crews lives. There's no guarantee he would even learn something from this fight, and that ability may or may not help him against Kaido. The crews survival this arc should be their top priority, and he's not helping that cause right now. And according to his own knowledge, he knows Brulee knows about the meeting spot, the rest of the crew don't. So they will be heading to cacao right into a trap unless he were to warn them, but chose to fight instead and let them deal with whatever mess happens when they reach cacao.
And of course if he were to lose, Katakuri would now have access to Brulee and would be waiting there for them instead. If he had left to find a mirror on 1 of the tart ships or even Bege's ship, they could escape without heading to the potential ambush in cacao.
–- Update From New Post Merge ---
I don't think there gonna be any apologizing really with anyone of the hero side.
I don't expect any major bursting down into tears type of apology like Usopp, as that doesn't fit nor did anyone commit some terrible crime where they need to do that.
But I do expect some characters to just say sorry. Nothing major. Sanji will say sorry for hitting luffy, nami and chopper may say it since they felt guilty back on zou, luffy should say it when he sees the state of the sunny being damaged and possibly injured crewmates. And if pound and pedro stay dead, maybe some apologies thrown in there.