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?
The Times When Jiraiya was Offered to be a Hokage
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 Konoha's chief counselors and the ruler of the Land of Fire to be the fifth Hokage. And still, he refused and nominated Tsunade instead. Not long after Pain attacked Konoha, which left Tsunade bedridden due to severe exhaustion as she tried to heal every injured person in the village, the talk about a new Hokage came up. Jiraiya had passed away at the time, but even in his death, his name was still mentioned as a great candidate for Hokage. However, since he was no longer in this world, the job fell onto Danzo instead.
Jiraiya's Deep Sense of Guilt
One of the main reasons why Jiraiya stubbornly refused the position of Hokage was due to his deep sense of guilt, particularly regarding Orochimaru. The relationship between Jiraiya and Orochimaru is highly similar to Naruto and Sasuke. They are akin to brothers, rather than simple friends or teammates.
So the fact that Orochimaru turned out to be a traitor and a dangerous shinobi who strayed so far away from the proper Shinobi’s way caused a deep sense of pain and guilt in Jiraiya's heart. In his mind, how could he become a Hokage, an entity who is supposed to guide and protect the whole village, when he couldn't even guide and protect his best friend and brother.
Jiraiya is Always on the Move
As mentioned in the previous section, Jiraiya was feeling guilt over his inability to prevent or even stop Orochimaru from becoming a shinobi who would frequently conduct experiments on people. As a way to redeem himself, Jiraiya would track down every move made by Orochimaru, including during his brief time as an Akatsuki member.
In order to do this, Jiraiya has to spend the majority of his time away from Konoha. As time went by, he also came to love this on-the-road lifestyle. After all, as a writer, a change in scenery is always a good source of inspiration. So as a man who spends the majority of his time traveling from one place to the next, it is virtually impossible for Jiraiya to take on the mantle of Hokage.
Inferiority Complex
Up to his very last gasp, Jiraiya viewed his life as nothing but a collection of failures. He failed to steal Tsunade's heart, he failed to save both Orochimaru and The Third Hokage, and he also failed to properly guide his student, Nagato. Other people may see him as a legendary shinobi with tons of unbelievable achievements. However, the man himself views his worth according to the things that he failed to achieve in life. This inferiority complex prevented him from actually taking on a role that required him to be responsible for many people's lives. On the other hand, Jiraya wouldn't hesitate to plunge headfirst into a dangerous mission and risk his own life in the process, which is exactly what he did when infiltrating Pain's hideout.
All the reasons above have nothing to do with Jiraiya's ability as a shinobi. Because everybody, including Jiraiya himself, knew that based on pure ability alone, Jiraiya was often more than qualified to be a Hokage. But as a man who has experienced so many painful things throughout his life, Jiraiya knew that it took more than raw power alone in order to be a great Hokage. One might argue that Jiraiya is simply being too hard on himself, but to him, there's no way he can be a great leader if his mind is still filled with guilt and insecurities. Taking the job with such a state of mind is a disservice to the people of Konoha, which is why he refused to be a Hokage.