WARNING: The following contains spoilers for My Hero Academia Chapter 337, "A Disposable Life” by Horikoshi Kohei, Caleb Cook, and John Hunt, available now in English from Viz Media.
If anyone were asked to list some of My Hero Academia's more... difficult characters, it's highly unlikely that Shoto Todoroki would rank near the top. He's best known for his laid-back, almost apathetic, attitude towards most of the goings-on around him, and yet he has a surprisingly insubordinate streak. Shoto's proved time and again, including in the latest chapter, that he can get about as disrespectful as even Katsuki Bakugo.
The first time Shoto displayed this particular trait was after he, Izuku Midoriya, and Tenya Ida defeated the Hero Killer, Stain. It was a noble act but in their haste to save lives, the trio didn't realize that their actions violated laws that prohibited unlicensed heroes from harming others with their Quirks. The person who had the misfortune of informing them about their transgressions was the Hosu City Chief of Police, Kenji Tsuragamae, but even that title wasn't enough to tame Shoto's sharp tongue.
Right after Kenji addressed them, Shoto angrily rebutted, tightly claiming that lives would have been lost due to their inaction. When Kenji seemed unwilling to see his point of view, Shoto called him a dog. Seeing as the Chief of Police possessed a heteromorphic Quirk that gave him the appearance of one, Shoto's insult must have been doubly offensive. Shoto apologized after Kenji made it clear that he didn't intend on punishing them but the damage, if any, had already been done.
The next time Shoto's impertinent side showed up was his first day at Endeavor's agency. After Endeavor assessed both Izuku and Katsuki's strengths and weaknesses, he dismissively walked away from Shoto because he assumed his son was there just to learn his most powerful move, Flashfire Fist. Shoto asked why he hadn't gotten a turn yet and without waiting for a go-ahead from Endeavor launched into a monologue of his own.
He explained how misguided his decision to ignore his Fire Quirk was and his journey towards realizing his folly before finally revealing why he'd decided to work with Endeavor. He'd come to use his father; not because he was interested in mending their relationship but because Endeavor was the quickest means to his end of becoming a powerful hero. Finally, he mentioned that he'd never admired Endeavor and told his father not to put on a parent act in front of his friends. In this case, his outburst was understandable but it was still rather rude.
Shoto's latest run-in with an authority figure happened during Yuga Aoyama's interrogation. Following Yuga's reveal as the UA traitor, Principal Nezu asked if the 1A students could excuse the adults conducting the interrogation. Shoto simply refused his request. It was a polite enough reply but taking into consideration the difference in status between principal and student, the exchange becomes a lot more disrespectful.
Though these situations may paint a picture of a very badly behaved Shoto, that is quite far from the case. He's normally very polite to classmates and superiors alike but like anyone else, he can lose control of his emotions sometimes. Shoto just happens to be more forthright than the average person and he doesn't lose this trait no matter who he happens to be talking to.