Luffy defeating the strongest fighters is not part of his dreams nor of his set character arc. It's just a coincidential part that simply happens because they're standing in the way of his actual dream.
However, even if Mihawk were stronger than Big Mom, Luffy will still be defeating the strongest fighters, since Big Mom is going down before the likes of Blackbeard or the Gorosei anyway, Mihawk could just rank anywhere in the middle. Either way, Kaido is the strongest and he's surely going down now by Luffy's hand. It's okay for at least one of the top tier fighters to go down by someone else's hand.
There is no way in the One Piece world to prove that you're more skilled with a sword without defeating other people, which is what the whole deal with Zoro's dream has always been about: defeating the strongest to prove that he's the strongest, not showing off in some weird skill competition.
I'll never understand why despite the overwhelming hype given to swordsmen that also never tried to become Yonkous (Rayleigh and Oden) and even swordsmen that have become Yonko (Shanks) some fans have trouble imagining Mihawk as at least potentially Yonko-level. For all we know, Shanks, too, could be stronger than Big Mom. No matter how peaceful his ways are, he must be on their level to take some territories and not be eliminated by the others, so there's no definite proof to say how Shanks ranks between the other Yonko.
Not to mention Big Mom has bothered learning sword skills and wields a sword for a reason and these are so far some of her most devastating attacks. If a character surpasses her in swordskill (which includes CoA applied to the sword, as we know that this is part of swordsmanship), she wouldn't have an easy time against the guy, and she could even logically lose. It'd come down to the rest of her skills, but so far I haven't seen Zeus or Prometheus as being much stronger than her strength with Napoleon. If someone is superior than her at using her weapon of choice (and thus, at applying CoA on the offensive as well), said person is a good candidate to making her bleed.
It can definitely be argued that Big Mom would win, but there's nothing plain stupid about saying otherwise.
Luffy himself said he wants to take on the Yonkou in Punk Hazard and was upset when Usopp said Luffy could become the Pirate King without needing to clash with the Yonkou. He wants to fight them, and not just because they're obstacles.
I'm using Whis's logic. But also, it doesn't make sense for Luffy to not take out the strongest person, according to Whis's logic, as he's trying to be as strong as possible to protect his loved ones. Otherwise as long as Luffy takes out at least one Emperor, it doesn't really matter because he has to show he can challenge an Emperor and not lose outright. I think we agree here.
Zoro's dream is to be the strongest swordsman, not the strongest fighter. Him going against people who aren't swordsmen or fight primarily or solely with swords doesn't help him much, and to boot, Zoro has almost always gone up against sword users. Plus, Mihawk's title is the World's Strongest Swordsman or whatever, it's not World's Strongest Fighter. Swordsman is specific enough for me to acknowledge that Mihawk's renown for his swordsmanship, not for fighting in general.
Shanks
is an Emperor though, so it's not hard to believe he's at least strong enough to compete with the other Emperors, especially with his tiny crew. If Kaidou for example wasn't an Emperor, I wouldn't consider him strong enough unless proven otherwise even with the WOrld's Strongest Creature or something as his title.
If BIg Mom beat Mihawk and used everything in her arsenal that wasn't related to swords to win, I wouldn't consider her the superior swordsman unless she was still using swords. That's all it is to me, fighting using that skill, probably with devil fruit involved as well.
If Luffy beat Mihawk on Marineford for example, would you consider Luffy the World's Strongest Swordsman as result?
Has it ever crossed your mind that the 5 up there are stronger than him?
Beside there are countless strong people who are not up there also, because it's not their fight, the narrative is pretty clear that the most powerful young generation of pirates will come and beat Kaido, and as we know the most powerful rockies who want to beat Kaido are all up there with the exception of Drake
Irrelevant. Especially when Jinbei is still a powerhouse who can deal out damage in different ways, as he did against a surprised Luffy.
Who else is strong enough to take on Kaidou or Big Mom without dying within a minute?