Is clearly showed on this passage I have closed read on the prisoner of Azkaban the little "respect", consideration that students at Hogwarts have upon their teachers which most readers don't notice. The students (Children) seem to be on a higher position than the teachers (Adults)  with more liberty to commit errors and to be forgiven. However, the teachers are in a continuing observation. They do one thing out of the normal and they are out. 
     
Harry Potter, Hermione and Ron do not have the "fear" most student have upon teachers. The capitalization of Harry's words- " YOU'RE PATHETIC!" Harry yelled.- when talking to Snape , one of the most feared and "respected" teachers at Hogwarts, clearly shows how confidents Harry and the others have on themselves. How because Dumblendore is on their side and is fooled by them, it means that their won't ever be punished and they can do whatever they want. Others students could not even think on confronting a teacher like those, Harry, Hermione and Ron, are doing. And not teachers could let them confront them either as they letting those three. This is all because they are privileged. Is not Harry anymore the only one who can do and don't do whatever he wants, its now the other two, his friends, Hermione and Ron that have also start doing as they want. On the other hand, we have the teachers, Snape and Lupin. Firstly Snape as I said before, is one of the most "respected" and feared teachers at Hogwarts but for Harry, Hermione and Ron , he is just one of a million, one among the others and what he says or order them to do is something they don't take on consideration. Not even Dumblendore listens to Snape's words. Snape who since the beginning didn't trust Lupin - "I've told the headmaster again and again that you're helping your old friend Black into the castle, Lupin, and here's the proof.-"  thinking that he will probably listen to his words, but once again this show that Dumblendore doesn't trust his own staff or doesn't believe at all everything they have to say, is like if what they think or say do not count at all, but if instead of Snape,  were Harry, Hermione, Ron or other student, Dumblendore will have listened to them because once again as I said before, students are the privileged.
     
Most readers don't notice how students at Hogwarts most of the time don't get punished when they do something they should clearly be punished from and how they influence the headmaster, Dumblendore, most of the time. On the other hand, we have the teachers, who It doesn't matter how right they are, or the proofs that they  have about whatever. They definitely won't be taken as serious as the students and that is something very unusual. There is no school like Hogwarts in the world. A school in which students would raise their voices to the teachers, without being punished. A school in which students would hit , in this case with their wands, teachers without being punished either. A school in which teachers are the ones who should control what they say or do to students. We can see by looking at this passage that at Hogwarts the students (young) are above the teachers (adults), and that is something that most readers don't see, this is important because it explain the actions of most of the students at Hogwarts and most importantly it explains why Harry, Ron and Hermione "keep searching for troubles". All because they know that they wont get punished because they are the heros, the ones who run the school like most of the students. 
     
This is not something that is just started at Hogwarts. Even when Snape, Lupin and Sirious were at Hogwarts, it was like this too. For example Lupin and Sirious, almost killed Snape when they all were students at Hogwarts, those two, including Harry's dad, were not punished for what they did but they were forgiven. But what if Snape himself had killed Harry because he would not get out of the way trying to protect, Lupin and Sirious, or simply used his wand against one of them, Harry, Hermione or Ron. He definitely will be kick out of the school even though he had told them to get out of the way. But it wasn't the case. Ron, Hermione and Harry, were the ones who used the wands against a teacher, who is supposed to be superior than them and from whom they should have respect or had listened when he told them to let Sirious and Lupin to him, but those three knowing that they could do whatever they want and it wont be consequences, didn't care about what Snape had to say. They don't listened to anybody but themselves and that's something unusual when talking about the relation between teachers and students. We seem teachers as our "parents", adults from who we should take advices and listen to what they have to say. People from whom we learn about life and in the case of wizards teachers are their "masters". But especially for those three, Ron, Hermione and Harry, the only teacher they respect so far is Dumblendore. 
      
If we read at this passage more than once, we can also notice that the relation between young and adult is practically the same as students and teachers in which the first ones are above the other. This passage shows clearly how privileged the students are and on the other hand how the teachers are below them.

