The Lost Marauder
At the beginning, there were four Marauders, led by two inseparable friends: James, Sirius, Remus and Peter, a.k.a. Prongs, Padfoot, Moony and Wormtail.
Peter Pettigrew: We know that he attended Hogwarts with the other Marauders, and took part in the making of the Marauder’s Map. After Hogwarts, he moved on to become one of Lord Voldemort’s Death Eaters. He then “blew himself up” and spent the next twelve years as Ron’s rat Scabbers.
James Potter: After graduating from Hogwarts (assuming he did), he served as a member of the Order of the Phoenix. We do not know what he did for a living (unless Order members get pay checks), but we know he had the potential to do anything (he and Sirius were very brainy). We don’t really know anything else he did in between Hogwarts and Voldemort’s attack. For the twelve years after Voldemort’s banishing, he was dead, and will remain so.
Sirius Black: James’s best friend, he apparently graduated Hogwarts with him and, like James, we know he had the potential to do anything. He became imprisoned in Azkaban around the same time Peter became Scabbers.
Remus Lupin: We know he attended Hogwarts, was a prefect, and was obviously smart. We know he was a werewolf. What we don’t know are his whereabouts during those twelve years after James’s death. Everybody else’s story checks out:
Where was Lupin? We can assume he must have had some past experience in either teaching or Defense Against the Dark Arts to get the position at Hogwarts those twelve years later. Twelve years is a long time, so I don’t believe that he was “in training” to become a teacher. And so returns our question: where was Lupin? We know he never tried to contact Harry, and apparently he never tried to contact Sirius (why would he?). During those twelve years he thought two of his best friends were dead and the one responsible was in Azkaban.
Where in the world was he living, who was he with (did he have any other friends?), and was he teaching or did he have another job? Well, we know from past DADA teachers some of the things that would qualify you for the post.
Professor Quirrel: Assumingly, he had prior experience to DADA either through teaching, or practical experience.
Professor Lockhart: Well, we all know that he was, to be blunt, a fake. But Dumbledore hired him because he thought that he worked as someone who protected wizards from “beasts” such as Yetis (Year with a Yeti), Werewolves (Wanderings with Werewolves), and Banshees (Break with a Banshee).
Professor Moody: An Auror, so assumingly dealt with that sort of stuff regularly.
Professor Umbridge: Elected by the Ministry, no apparent talent whatsoever.
So we know from these teachers some guidelines of what Lupin needed to be a DADA teacher: teaching experience, beast experience, auroring, or being a favorite undersecretary to the Minister (highly unlikely). Which of these suits Lupin? Well, since we know that he’s a werewolf, perhaps he could have had some experience dealing with beasts and we know that his curriculum was mostly Dark creatures.
We also know that Dumbledore must have kept in contact with him during those twelve years (or at least some of them), as he trusted Lupin and elected him to come back.
After losing two friends to the Dark Arts, wouldn’t Lupin want some sort of revenge or to get out there and fight? So there’s another theory, maybe he was an Auror.
No matter what, we know that JKR has a knack for slipping things into place smoothly, and we also know that she includes and excludes things for a reason. For that reason, I’m pretty sure that Lupin’s “absence” during those twelve years will have something to do with the future books.