There's a lot of talk about why Snape was denied the Defense Against the Dark Arts teaching job, but why did Snape want it in the first place?
He is shown to be very skilled at two branches of magic: Occlumency (enough to resist Voldemort himself) and Potions (as a student he figuratively and literally wrote the book on the subject) – and his attitude in the notation in the Potions textbook implies he took great pride and enjoyment in his Potion skills in particular.
True, he had an interest in the Dark Arts as a student, but surely he realized he would never be able to do "Dark Arts research" just by holding the teaching post (also, per JK Rowling Why did Snape love dark Magic so much?, Snape was interested in group membership more than the Dark Arts themselves). Furthermore, it was subtly implied that he lost his interest in the Dark Arts after he lost Lily because of them. Finally, Harry's favorite subject was Defense Against the Dark Arts, and as petty as it is, Snape maintained the sort of pride that would not enjoy pining for the teaching position that was Harry's favorite.
So why would he want the job at all?