I know of this question
Why did Snape want the Dark Arts job?
But my question is a bit different.
I want to know even when Snape knew that the dark arts job was jinxed by Voldemort himself and nobody lasted more than a year in this job, why would he want this job?
Namely, Headmaster of Hogwarts.
This explanation holds for the year that Snape was actually appointed DADA Professor. Why he wanted the post before then is explained further down.
The summer before his appointment as Defence Against the Dark Arts teacher Snape discovered that the current Headmaster, Albus Dumbledore, had only a year to live.
"You have done very well, Severus. How long do you think I have?"
Dumbledore's tone was conversational; he might have been asking for a weather forecast. Snape hesitated, and then said, "I cannot tell. Maybe a year. There is no halting such a spell forever."
(Deathly Hallows, Chapter 33, The Prince's Tale).
Snape therefore knew that there would be a vacancy for the position of Headmaster within a year. It was Dumbledore's intention that Snape should take this position in order to safeguard the Hogwarts children.
"Lord Voldemort foresees a moment in the near future when he will not need a spy at Hogwarts?"
"He believes the school will soon be in his grasp, yes."
"And if it does fall into his grasp," said Dumbledore, almost, it seemed, as an aside, "I have your word that you will do all in your power to protect the students of Hogwarts?"
Snape gave a stiff nod.
(Deathly Hallows, Chapter 33, The Prince's Tale)."And Severus, if you are forced to take part in the chase, be sure to act your part convincingly...I am counting upon you to remain in Lord Voldemort's good books as long as possible, or Hogwarts will be left to the mercy of the Carrows..."
(Deathly Hallows, Chapter 33, The Prince's Tale).
Bearing in mind this wider picture, it doesn't matter much whether Snape spends his final year as a full-time teacher teaching Defence Against the Dark Arts or Potions. But, since a position needed to be found for Slughorn and since Snape had wanted to teach DADA for as long as anyone could remember, Dumbledore gave Snape the Defence Against the Dark Arts job.
The DADA curse and Snape's desperation to hold the position were both widely known.
Professor Snape, the Potions master, was staring along the staff table at Professor Lupin. It was common knowledge that Snape wanted the Defence Against the Dark Arts job, but even Harry, who hated Snape, was startled at the expression twisting his thin, sallow face.
(Prisoner of Azkaban, Chapter 5, The Dementor)."Well, there's one good thing," he said savagely. "Snape'll be gone by the end of the year."
"What do you mean?" asked Ron.
"That job's jinxed. No one's lasted more than a year...Quirrell actually died doing it. Personally, I'm going to keep my fingers crossed for another death..."
(Half-Blood Prince, Chapter 8, Snape Victorious).
So, taken together, Snape would have known about the curse. It didn't faze him, though. He knew that he had a good shot of becoming Headmaster under Voldemort if he played his cards right. Even if Dumbledore were to confound his diagnosis and live for more than a year the curse need not bother Snape. He can leave Hogwarts and become a full-time Death Eater (and spy).
What about all the previous years when Snape still wanted the job?
It's true that Snape wanted the job, even before he knew that he might go on to become Headmaster. If Snape knew about the curse and had no clear idea what he would do after the DADA job, why would Snape still seek after the position?
Presumably, he assumed that he would be able to stay at Hogwarts. He can simply go back to teaching Potions come the end of the year. We know that he liked it at Hogwarts and that he enjoyed the comfort and safety of the castle. And, despite his obsession with Defence Against the Dark Arts, he obviously also loves Potions. He was an expert Potion-maker with a decade of experience in the job. There's no reason why, if he'd hired a temporary or inferior Potions teacher, that Dumbledore wouldn't give Snape his old job back at the end of the year. Ron at least thought that that was what might end up happening.
"He might just go back to teaching Potions at the end of the year," Ron said reasonably. "That Slughorn bloke might not want to stay long-term, Moody didn't."
(Half-Blood Prince, Chapter 8, Snape Victorious).
I can't confirm his reasoning from any specific quotation from the book, but it is very likely that Snape believed he could break the curse. He would have no motivation to break it for other teachers, but had he held the position himself, he would have likely done everything he could to break the curse. The curse would have already been a decade old at any point in Harry's Hogwarts career, plus Snape had access to libraries and continued learning in order to research how to break it.
It is not unreasonable to believe that Snape had powers the Dark Lord didn't know of. For instance, Snape was the superior legilimens and Voldemort never understood Snape's motivation.
Also, to some extent, Snape broke Voldemort's curse on the ring horcrux/hallow. He told Dumbledore that he could have done more had Dumbledore a.) Called him sooner, and b.) Not actually worn the ring.
Snape's Dark Art powers definitely rival Voldemort's.
Loyalty to Dumbledore.
Dumbledore needed Slughorn, which meant Snape had to step down as Potions Master. The only plausible way for that to happen, without exposing to Voldemort that Snape was on Dumbledore's side, was for Snape to be given the job he'd always wanted: the Defense Against the Dark Arts position. Accepting the position was risky, but not suicidal - Slughorn was only staying a year, so Snape could reasonably expect to return to his old job after that, making the curse moot.
It is also plausible, though in my opinion less likely, that having Voldemort's consent to take the position meant the curse would not take effect. Magic doesn't usually work quite like that in Harry Potter, but it isn't entirely out of the question.
Of course, I'm assuming here that you're talking about Half-Blood Prince. If you meant to ask why Snape originally asked for the Defense Against the Dark Arts job, well, for one thing we don't know for sure that he did - it was certainly rumoured, and he told Bellatrix that he had, but he might have been lying.
It is also possible that he did not at that time know about the jinx.
Although the jinx had already been in place for ten or so years when Snape first took his position at Hogwarts, that was during the First Wizarding War; many wizards lost their lives in that time, and those with the skills necessary for the Defense Against the Dark Arts job would be particularly at risk, so it would not necessarily have been obvious that whatever misfortunates may have befallen them were due to a jinx rather than to the hazards of war. Only once the war was over, and DADA professors continued to suffer unlikely misfortunes anyway, did the presence of the curse become more obvious.
It is my opinion that Dumbledore was already aware of the curse, and that may well have been one of the reasons he did not give Snape the DADA position. That's just speculation, though.
Maybe he actually didn't want it the other years. It might just be a rumour circling around.
The only time he's allowed to take the position is when Dumbledore already knows that Snape will have to kill him in the end of the year. Since the job is cursed anyway, it's a very convenient way of finding a teacher to a subject that's been filled with crap-teachers for most of the years.
Unfortunately, I do not have any quotes to back this up. But again, is there any canon material from Snapes POV that he actually did want this job before year six?
Maybe, if there is a real curse, Snape asked Voldemort about it and got an answer along the lines of, "It does not affect Death Eaters", or, "Here's how to break it".
Or maybe the curse is a myth. At least two people who appear to be affected work for Voldemort and thus should not be affected, unless Voldemort being very stupid or thinks he is going to get what he needs before the year is done and is willing to take a cursed job because of it.
The curse might just be a fluke. The rumors of a curse made only the desperate take it and the desperate do not keep the job for long, thus making the curse a self-fulfilling prophecy. Weirder things have happened in real life. Look long enough for a curse or a haunting and one is going to find one.
I disagree with the idea that Snape knows of the curse. Dumbledore always knew about it, so he didn't allow Snape to teach Defense because he would have presumably left the school. Once Dumbledore realized he would be dying within year's end, he was all right with the potential of Snape leaving, even if it didn't work out that way. So Snape never was aware of any curse, and Dumbledore allowed him to take the job when it fit into his plans. It's certainly true there were many rumors of a curse throughout the books, but Dumbledore never confirmed that to Harry until well into Book 6 in the chapter Lord Voldemort's Request, so it seems unlikely anyone was truly certain a curse existed, and much less likely that Lord Voldemort was the one who cursed it.
In Potions, Snape puts his heart and soul. In DADA he knows "from and to" exactly those spheres that are useful for him. The true vocation of Snape is still Potions, not DADA.
However, every year, from the time he joins Hogwarts, he submits an application to Dumbledore for the post of DADA. And Dumbledore denied it, thus that everyone knows about it. Why would he (and Dumbledore) need this? There is only one answer to this question - this is necessary to create the impression for Voldemort (and, for greater reliability, the entire magical world in general) has the impression that Snape and Dumbledore don't have everything smooth in their relations. This assumption is documented from the mouth of Snape himself.
Further. The impression is created so well that bought by Lupine and kindly invites Snape to conduct a lesson of DADA in his absence. Snape, as part of maintaining the legend, is forced to accept this "gift". He needs him? No. Is he ready for the lesson? No. He has a lot of things to do, he has no time to refresh all this nonsense for preschool children about some Kappas, Hinkypunks and other Grindylows. They never interested him and didn't interest now. And in general he was angry at Lupine as a thousand devils.
