This is why I put Jiraiya into one of my favourite Naruto characters.
He's offered with such important position of being a hokage by the advisers and the feudal lords. The reason is simple, he's a Sannin. It means he has a notable reputation of being one of the strongest shinobi, being capable of protecting the village and the lords' power and authority within the country, The Land of Fire, due to his own strengths and skills as one of the legendary Sannins.
He had every right to take the offer. He had every chance to raise himself to the power. But what? He turned it down. Simply turned the golden opportunity down. It's something that any other capable ninja like Orochimaru or the likes of Danzo would grab if they're him.
Jiraiya assumed he's not destined for being a hokage just because he viewed himself having no natural abilities in handling the internal and external political affairs because his personality (see picture number 4 as he states himself. This long explanation is just my interpretation). Alternatively, it could be his apathy towards politics since he hyperfixated on shielding Konoha from threats and indulged in writing his own novels (in my opinion).
Even when faced with Jiraiya's objection, it's not without his own final resolution. It's something I see as his sagacity and prudence. He's not just staying silent, waiting these elders to offer other solutions. He tried to give one. After he analysed this entire discussion with these advisers and them mentioning "Sannin", Jiraiya quickly thought of another shinobi who shared this title with him and Orochimaru. The person is Tsunade, someone he deemed worthy because she bore no reputation of being a criminal like Orochimaru besides being a powerful kunoichi.
Without hesitation, he proposed his idea of making Tsunade the next hokage to the advisers. To him, it doesn't matter if they're a man or a woman. Gender has nothing to do with this. If these elders want a sannin who's capable of managing political affairs whilst simultaneously having love for the village with its citizens and possessing powers to protect them, the only one he can present is Tsunade no matter gender.
(Naruto episode 81)
