In Harry Potter and the Prisoner of Azkaban, Remus Lupin (David Thewlis) teaches Harry (Daniel Radcliffe) how to conjure a Patronus charm, but his own Patronus is never seen - here's why. The Patronus is important to a witch or wizard's identity: Harry's is a stag (like his father James' Patronus), the Weasley twins (James and Oliver Phelps) both have magpies (hinting at the UK saying "one for sorrow, two for joy"), and Snape's (Alan Rickman) is a doe, which symbolizes his lifelong love for Lily Potter. In Lupin's case, the answer is an obvious one: a wolf.
When Remus was invited to teach at Hogwarts, only a handful of teachers knew he was a werewolf - no parents would want their children anywhere near one. In fact, Remus only accepted the position after Dumbledore (Michael Gambon) promised him an endless supply of Wolfsbane Potion, which Snape would unenthusiastically supply, restricting Lupin's monthly transformation to an ordinary wolf. It had always been Remus’ worst fear that he would kill while out of his right mind, and a school full of students was the worst place to be in this respect. There was a great stigma surrounding werewolves: Lupin receiving the Order of Merlin posthumously for his Order of Phoenix contributions was the first step in lifting this stigma. Unfortunately, during his life, Remus had to hide his identity as a werewolf - and thus his wolf-shaped Patronus, too.
Stigma is not the only reason Remus Lupin hides his wolf-shaped Patronus, as the wolf is generally a reminder of his pain and tragedy. When he was only four, Remus was bitten by the notorious Death Eater and werewolf Fenrir Greyback (Dave Legeno), who wanted to get his revenge on Remus' father Lyall for trying to arrest him and calling werewolves "soulless, evil, deserving nothing but death." Lupin's family had to live with this tragedy, keeping their son isolated for his (and everyone else's) safety. Remus lived a poor, itinerant life until James Potter took him under his wing. When Lily and James Potter died, Remus went back to a lonely, miserable life, unable to hold a job for more than a few months (until people figured out his condition). Lupin thus hates his Patronus shape, as J.K. Rowling wrote (via Wizarding World), "Everything wolfish disgusts him, and he often produces a non-corporeal Patronus deliberately, especially when others are watching."
Fellow Order of Phoenix member Nymphadora Tonks (Natalia Tena) was the first one to declare her love for Remus and accept him for who he truly is. This came as quite a shock to Remus, who was used to people hating or avoiding him. Throughout their marriage, Remus swung constantly between elation and terror of infecting Tonks with the stigma attached to him. When Tonks got pregnant, Remus even ran away, unable to face the horrors of raising a son with lycanthropy. Eventually, Harry talked sense into him, and Lupin and Tonks stayed close together until their deaths.
In The Half-Blood Prince, Tonks' Patronus changes from a hare to a wolf, symbolizing her strong love for Remus. Perhaps this helped change how Remus viewed his own wolf Patronus, as someone else's love for him meant he could start loving himself, too. Rowling commented that "Lupin’s condition of lycanthropy was a metaphor for those illnesses that carry a stigma, like HIV and AIDS." Throughout the Harry Potter saga, Remus Lupin fights his affliction and shuns any reminder (including his Patronus) of the tragedy he's had to live through. In the Harry Potter movies, David Thewlis (who arguably plays the Coens' best villain in Fargo) does an excellent job at portraying a conflicted, at times self-hating but ever-kind character.
