In the databooks, it has been said that zoro is nearly as strong as Luffy. Some fans even claim that he is stronger. But then, why does Luffy deserve to be captain of the straw hat pirates?
It can't merely be because Luffy saved zoro's life all those years ago. If helmeppo or someone else saved zoro, would zoro have followed him? Would zoro have followed any bum-ass who untied him? Obviously not, obviously Luffy is special. So what is so special about Luffy?
Well, Luffy himself answered this in chapter 90 of the manga, which is aptly titled "what can you do". In it, Luffy admits he can't use a sword, cook, navigate, or tell lies. Arlong mocks Luffy asks him what Luffy can do. Luffy responds with telling Arlong that he can beat him.
I think the special thing about Luffy is something that is highlighted in almost all of his fights. That is his resilience to defeat. Whereas Zoro is comparable in strength to Luffy, resilience to defeat is an attribute that has NEVER been attributed to him. Think about it, an integral part of Zoro's character is basically the opposite, zoro is averse to defeat. He isn't afraid of defeat don't get me wrong, but he would rather die before failing and this ideology allows him to undertake immense amounts of pain that even Luffy can't handle. The most famous examples of this are thriller bark and wano kuni.
The one time Zoro did flat out fail was against mihawk in east blue, after which he basically attempted suicide by telling Mihawk to slash him across the chest, and subsequently started crying due to shame. Now I don't want zoro fans to misunderstand me, this isn't an attack on zoro, but I think it is important to note: Luffy would never do this.
Luffy doesn't give a shit about defeat. He doesn't care how many times he is defeated or how many time someone makes a fool of him. Luffy is rubber and he will always bounce back. Whereas Zoro's fights focus on Zoro enduring the pain to never lose, Luffy's fights focus on him having the will to fight in the face of failure. This is why Luffy is such a good protagonist, because he isn't zoro, the man who never loses. He loses multiple times, every single arc. And yet he always has the strength to keep on fighting.
This is why Luffy is such a lovable character(to both the fans and to other characters in the story), and why imo Luffy deserves to be captain. In the biggest arcs of the story, the main villains are always far stronger than Luffy. Sometimes Zoro gets a villain stronger than him, but the gap is nowhere as close as Luffy and the main villain. This is the truth behind Luffy's statement to Arlong. Luffy is the only one who can beat these big bad villains(ect. Crocodile, Doffy, Kaido, ect.) because he is the only one with the willpower to keep fighting in the face of crushing defeat.