I'm going to begin every theory I make by saying I hate presenting theories and I hate talking to people about them! Why? Because I never get positive feedback. Ever. However, I'm going to point out that you should expect crazy theories for a crazy story like One Piece. What are you expecting? Everything to be perfectly reasonable? Ha! That's a laugh.
I am presenting a theory about why Zoro does not have Conqueror's Haki. I would say this should end the discussion on whether he does or not, but I'm sure other people will find ways to continue the argument.
To explain why Zoro does not have Conqueror's Haki, I must discuss Zoro's Armament Haki Specialty, and how it relates to what occurred between him and Kaido during the interaction when Kaido questioned Zoro about being able to infuse his attacks with Conqueror's Haki.
Zoro's Armament Haki Specialty is based on enhancing his physical body by combining it with a subtle body of another living entity. Zoro has combined his body with gorillas, tigers, dragons, and other various creatures defined as living entities. Zoro has combined his body with something beyond normal living creatures. The Demon Spirit "Asura" has superior qualities because of a strange rule. The rule that defines the Demon Spirit "Asura" as possessing superior qualities is based on where the living entities reside. Gorillas, tigers, dragons, and other various creatures live in the material world, but the Demon Spirit "Asura" lives in the immaterial world. Therefore, it bestows Zoro with divine qualities instead of non-divine qualities derived of normal living entities. The Demon Spirit "Asura" is not a normal living entity. The primary quality that the Demon Spirit "Asura" bestows upon Zoro is Conqueror's Haki. Secondary qualities include Nine-Sword Style which is enabled by creating an illusion from his spirit. Rather, an illusion of the Demon Spirit "Asura" comes forth when he is abiding by Cosmic Law during combat. Sometimes, he taps into this power accidentally. Recently, in one of the episodes he seemed to perform a Conqueror's Haki attack and knocked out a few people. That's not what happened... what happened is he temporarily tapped into the Demon Spirit "Asura" and used its Conqueror's Haki to knock them unconscious. It's not his own.
Therefore, the short answer as to whether Zoro possesses Conqueror's Haki is "no". He does not. However, the long answer as to whether Zoro possesses Conqueror's Haki is "yes, but it's not actually his own -- it's the Demon Spirit "Asura" who provides the Conqueror's Haki instead".
Other evidence includes that Conqueror's Haki cannot be trained. It is something that must be gained through the trials of a king regarded as the King's Dilemma. Sometimes, people are born with Conqueror's Haki, but that merely indicates that they already went through the King's Dilemma in a previous lifetime! The King's Dilemma develops when a King makes choices regarding the protection of his kingdom. The King may either hold peace as an ideal, or war as an ideal, and by choosing to pursue one or the other will determine whether a King will develop Conqueror's Haki or not.
With that said, the reason Zoro did not know what Kaido was talking about is because what Kaido was talking about was unknowable.
I know that sounds stupid as hell, but that's exactly what happened.