I agree that 'arrogant' is a judgement - it takes behaviour that can be described, and assumes the reason for that behaviour is that the child (in this case) believes they are better than everyone else.
If a student tries to correct the teacher that could be for a number of reasons. The teacher may be wrong. The student might think they know best about everything, but are wrong. It might be a topic with a number of different perspectives. The student might have poor social skills, and their way of asking for further explanation comes across as disagreeing.
I was badly bullied at school, and withdrew completely. About a decade later I ran into someone from my class in a completely unexpected situation (hundreds of miles away). Not someone I knew that well, but we had been in the same class for several years. He raved about how independent and confident I had been, how immune from the peer pressure he and others felt... in truth, I had been terrified to interact with anyone, and it took me years for my mental health to recover. Behaviour can have any number of explanations.
If the teacher has a problem with a child's behaviour, they need to be clear on what exactly the problem behaviour is, and what they want to see changed.
'Often disagrees with XYZ... they need to come and see me after the lesson if they have any queries about the way I present XYZ, otherwise it is a distraction for the other students' for example.
Assuming a reason does not help anyone.