Regardless of whether they are a werewolf or not, Arnbjorn will use little nicknames such as 'lambshank,' 'beef roast,' 'tidbit,' or 'hamhock.' He says not to take offense from the nicknames. If the Dragonborn is also a werewolf, however, he will immediately know and react a bit more amiably. He initially disapproves of the Dragonborn, showing a rude attitude, but after several successful assassinations, he begins to respect and even envy the Dragonborn.
He joined The Circle and became a werewolf prior to his expulsion. It is unclear what these methods were or how they were offensive, however, given his current status, it seems possible he used underhanded, duplicitous techniques that would have offended the Companions' sense of honor. He was asked to leave because his 'unorthodox' methods were offensive to other members.