We get why Christopher Herrmann (David Eigenberg) didn't get promoted to Chief when Wallace Boden (Eamonn Walker) left Firehouse 51. The character didn't have the experience needed to do the job, nor did he really spend the time to prepare to take on such a responsibility.
It was slightly disappointing to see him get earmarked for the gig, only to have an outside, Chief Dom Pascal (Dermot Mulroney), come in, but the more time has passed, the more we understand why. We think the character is ready to embark on the next chapter of his career, though.
Herrmann passed the captain exam

In season 13, Herrmann has taken more of a leadership role in the firehouse. He not only passed the captain exam, which is a huge feather in his cap, but he has worked directly under Pascal, who has, to his credit, been willing to advise Herrmann on the do's and don'ts of being a Chief.
Of course, these two don't always see eye to eye. Pascal requested that Herrmann stick by his side during the One Chicago crossover, and Herrmann responded by disobeying these orders and going into the field to help his friends. Pascal was a little frustrated, but there also seemed to be an implicit understanding that the desire to roll up sleeves and get to it is a Herrmann trait.
It will like be part of his approach whenever he's promoted. Then there's the 51 of it all. The actor who plays Herrmann, David Eigenberg, told TV Insider that the character doesn't plan on leaving firehouse 51, where he spent most of his career. He's going to stay put, and it's non-negotiable. He's not going to approve of a Pascal-sanctioned transfer in order to further his career.
The character is eyeing Dom Pascal's job

"He loves the firehouse. He does not want to leave the firehouse," the actor noted. "He wants to finish out his career. I don’t know how many years left he has. We just have to see." Eigenberg also spoke on the dynamic between Herrmann and Pascal, and how these two will likely be forced to duke it out for the 51 spot at the end of the day.
"I don’t think that Pascal’s going to be in that place and not that Herrmann’s watching him, but I think Herrmann would crush him if it got," Eigenberg told the outlet. "Because we were sussing him out. It takes time to know somebody." Plus, Pascal is starting to come apart at the seams due to the death of his estranged wife, Monica (KaDee Strickland). It's difficult to say how much longer he will be fit for duty.
In an effort to preserve full transparency, Eigenberg also noted that a firehouse run by Herrmann would have some "old school" tendencies that would need to be ironed out given modern day standards. Which, frankly, sounds like a mashup that would be wildly entertaining to watch.