It was recently revealed in the Bleach: The Thousand-Year Blood War anime that Ichigo's father, Isshin Kurosaki (then Shiba), was the previous captain of Squad 10, immediately proceeding fan-favorite character Toshiro Hitsugaya. But Hitsugaya was shown to be the third seat at the time, so how did he leapfrog past his lieutenant to take the captaincy?
Bleach series creator Tite Kubo occasionally weighs in on fan questions via Shueisha's "Klub Outside" platform, and one diligent fan, MShadow, translated the answers to these questions and shared them on the website Fanverse. One such question asked how Hitsugaya managed to become Isshin's successor, when it seems like the task should have fallen to his lieutenant, Rangiku Matsumoto. According to Kubo, there's a very simple answer: Hitsugaya had already obtained his bankai, and Rangiku hadn't.
Bleach's Captains and Bankai
It's been said that, generally speaking, it's necessary for a Soul Reaper to have trained and achieved bankai with their Zanpakuto in order to obtain the captain rank. The one known exception to this in Bleach is Kenpachi Zaraki, who hadn't even obtained the lower shikai when he joined. Despite his young age, Kubo states that Hitsugaya had already obtained bankai before even joining the 13 Court Guard Squads, which probably explains how he was able to skyrocket to the third seat while still being relatively inexperienced. When Isshin stayed in the human world with Masaki, it became necessary to replace him, but without a bankai, Rangiku wasn't up to the task. So, logically, they just went one step further down the chain to Hitsugaya, who did, and he was able to prove himself as captain. In another question, Kubo explained that Hitsugaya's bankai is not in a truly complete state yet, as he still has more maturing to do, and with it will come maturation of the bankai as well. He also clarifies that both Rangiku and Hitsugaya recognized Ichigo as Isshin's son in Bleach, but didn't mention it, possibly to avoid getting their former captain into trouble.
This also raises one other interesting point: it's apparently not necessary to have a bankai to become a lieutenant. While many lieutenants have been shown to have bankai, such as Renji and Ikkaku, others haven't even revealed their shikai, such as Nanao. It may in fact be the case that most lieutenants don't have bankai, and that it's actually pretty rare to see a lieutenant with a bankai. A Lieutenant is selected purely based on their captain's discretion, after all, so it makes sense that possessing a bankai ability may not be a major factor in the selection process for some captains. If some squads can even have co-lieutenants sharing the position, then why not lieutenants without bankai?
While achieving bankai may be the most important factor in becoming a Soul Reaper Captain in Bleach, the lack of one is apparently not able to restrict one's progress through the ranks up to that point. Mastering one's Zanpakuto is reserved for the best of the best--a group that apparently has long included Toshiro Hitsugaya.
Source: Fanverse