There are multiple ways you can deal with student arguing. They all have within them, though, be really clear with the students what the policy is. If arguing is not okay, never okay, then make that clear to students and set up a procedure that enforces that or helps reinforce that for you. And I'll give you a couple of examples.
The easiest thing I ever saw around arguing was a teacher in Arizona who, when her students would argue with her, or start to argue with her about something, she'd say 'Oh, no. I think you have forgotten, I argue by appointment only. If you'd like to make an appointment, put your name on the board and we'll set that up, but right now, do this'. And for her that worked, the students would be like 'Nah, never mind', and they just do what she asked them to do, because it wasn't worth making an appointment to argue with her later. They were really just trying to distract her and that procedure, that policy, took care of them trying to distract and got them back on task.
A more involved version of teaching students not to argue is something we call Arguing With The Ref or No Arguing With The Ref. No Arguing With The Ref is a policy where you teach the students that it's not okay to argue with you and what will happen if they do argue with you. So I might have a couple of students and I might have asked a student to stop talking while I am talking and she continues, so I move up my consequences hierarchy to the students name and the teacher look. So I say her name 'Sally!', and she stops for a moment and I think that's enough, I'm assuming the best about her and I move on, but five seconds later she's talking again. So I move up to a verbal warning, 'Sally, if you continue to talk while I am talking, you will have to move to the front of the room for the rest of the lesson'.
Now this is something that Sally doesn't want, so she says 'Mrs. Dearborn, I promise I'll never speak again in my natural born life', I say 'That's all right, Sally. Just while I'm speaking with be sufficient', and we move on with the lesson. I'm turning around to write something on the board and I hear 'Blop, blop', 'Sally, look what you have won. An all expenses paid trip to the front of the room. Come on down'. So, Sally, at this point, is very likely to argue with me, but if Sally does argue with me, then there will be a very clear consequence in place for that arguing. And this is, again, one of those things that we role-play with students, what Sally should do, and the best of all possible worlds is she should let me know that she disagrees with that decisions and you can set up a procedure for her to do this.
For example, you might teach to your students that if I make a decision and you don't agree with it, you can let me know that you don't agree, non-verbally, by giving me a particular hand-gesture, like this. For T, time-out, I need a teacher talk. So then when I ask her to move and she thinks I'm in the wrong and that she shouldn't have to move, she can give me the T, I can match it, I point, she moves. Later on, when I have time, I can call her up. 'Sally, you gave me the T, you wanted to talk about that decision what do you want to say?', so then she goes into this elaborate explanation, how she can prove that it wasn't her that was talking when I asked her to move, and I play the whole thing back, and I realize she might be right.
So I send her back to her original seat, but at the end of the lesson, I might debrief that procedure with the entire class. 'Class, during that lesson I asked Sally to move for talking, she didn't agree, so she gave me the T to let me know she wanted to talk about it, but she did, in fact, move. Later when we spoke, I realized I was wrong. It was not Sally who was talking. So she's back where she started. No harm, no foul'. In the meantime, I have also spoken with the student who did call out, who I mistakenly thought was Sally and I've dealt with that as well, so all is well there. But what I want to point out to you class is this, if Sally had argued with me, even though I was in the wrong, Sally would've gotten a second consequence, because in my class there is no arguing with the ref'.
Using those words, arguing with the ref, is something that works contextually at multiple grade levels, because all kids are familiar with referees and that you can't really argue with one, and so it works as an analogy in the class room. So whatever works for you, if that doesn't seem comfortable, that's okay, but think about how clear have you been about what your no arguing policy is. How do students communicate with you if they feel like they've been wronged, but not in the moment, later on how do they have the opportunity to discuss that with you? And then be a 100% consistent in enforcing that policy with your students, and you will see the arguing decline dramatically in your classroom.