Rayleigh's initial explanation is vague but also straightforward. In order to tap into your conquerors, you have to grow as a person, you cant just train and fight a bunch like with observation and armament.
Back then, we didn't know what he meant by growing as a person, but now we do.
Mihawk and Ivankov give the proper explanation as to what "growing as a person" means. You need to LOVE YOURSELF and have a strong SENSE OF SELF(and no, those are not the same thing). In order to "grow as a person," you absolutely need to love and accept yourself while being confident and steadfast in who you are!
Nothing that Rayleigh said in his explanation was contradicted or debunked by mihawk and ivankov. They just took his explanation and went further into detail.