Jiraiya is without a doubt one of the strongest shinobi in the Naruto universe. After all, along with Orochimaru and Tsunade, Jiraiya is considered to be a legendary shinobi from Konoha. As a matter of fact, one of the reasons why Itachi and Kisame didn't target Naruto during his training days is because Jiraiya was there. Itachi said that even if he and Kisame are to fight against Jiraiya at the same time, at most, they will reach a stalemate. Winning against this legendary shinobi alone is nearly impossible.
However, this raises the question, if Jiraiya was so powerful, why didn't he take the seat as the Hokage of Konoha? After all, a Hokage is supposed to be the strongest shinobi in the village. Well, the answer is he was actually asked to be Hokage on several occasions. Unfortunately, it is Jiraiya himself who flat-out refused to be a Hokage. So what's the reason behind his reluctance to take on the role?
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As mentioned before, there have been several instances in which Jiraiya was offered, or even downright appointed to be a Hokage, and yet he refused the job. The first time Jiraiya was asked to be Hokage was right around the time when the Third Hokage decided to retire. The Third actually prefered Orochimaru as a Hokage, after all, he was a highly gifted shinobi. However, Orochimaru at the time was turned into an incredibly dangerous and deranged shinobi, so The Third went with the next best option, which was Jiraiya. Jiraiya declined the offer and nominated his student, Minato Namikaze, instead.
The second time was after Orochimaru tried to invade Konoha and killed the Third Hokage in the process. Here, Jiraiya was actually appointed by both
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