Touched on this briefly, but decided to go more in depth since it seems to be a point that keeps getting brought up as a reason for why Carrot can't join. That being her relationship with Luffy. People claim that Luffy hasn't shown any interest in Carrot and as a result she won't join the crew. It's true that Luffy did have a significant relationship to most of his crew members before they joined, and I think the relationship between Luffy and Carrot has been gone about in a unique way, but it will still end up being significant and meaningful in its own way.
When it comes to Carrot's relationship with Luffy people always phrase it in a manner saying Luffy has shown zero interest in her as if the relationship is similar to that of grand fleet commanders with them showing tons of admiration and interest, and Luffy not really giving a shit. He hardly even remembers their names. Whereas the relationship with Luffy and Carrot is more of a mutual friendship, but the relationship not going much deeper than that.
When put into context however, the depth of that relationship makes total sense.
The kozuki and the minks have been waiting for Luffy and his crew for centuries yet Carrot has zero idea about their importance. To her, they are just her friends, not these people of prophecy, destined to change the world. At the moment, Luffy does not see Carrot as anything but a friend, and likewise, Carrot does not see Luffy as anything but a friend. However the final words of Pedro to Carrot are telling her to push on and that she will, one day, understand their true importance. How the straw hats are much more than just friends, and how they are on much more than just an adventure.
This moment of understanding that Pedro spoke of would perfectly parallel this moment from Jinbe:
A true comprehension of the greater picture and a pledge to take part.
This also parallels to Oden's journey:
Someone who had set out for nothing but adventure, exactly like Carrot, but upon encountering Roger he got a sense that there was something important about him and meaningful to their encounter and wished to find out more.
It's possible the reason Carrot and Luffy, despite being friends and having travelled together for so long don't have a deeper relationship is precisely because the significance behind the deepening of the relationship is a plot point Oda intends to address at a later point. Carrot's been set up to have an enlightened moment in the story where she fully understands what Luffy represents and will bring about and it's possible that her actions that follow with this understanding triggers a moment of great significance between the two.
I think it might not be a coincidence that Carrot hasn't had any of her cool moments in front of Luffy. Be it when she was able to jump in mid-air, jumped so high she could see across an entire city, took over the mirro-world, when she transformed into a moon lion werewolf goddess, when she solo'ed one of a yonko's fleets. Luffy's not been there for a single moment. Considering how others reacted, Luffy would go crazy over some of these things. It's possible Oda is holding back for the right moment in the narrative for the two to have a greater interest in one another.
Carrot isn't the only one that has yet to learn of the straw hats importance. All of the minks and the kozuki are in the same situation. But the fact that this major plot point is being told with her at the forefront of it speaks volumes to her overall importance in the story.
