Why do Viola and Feste seem to get along so well?

Their wit and intelligence makes them seem the perfect pair.

"Scene 1 finally brings Feste and Viola together for an interesting conversation that reveals a great deal about Feste's role in the play. Feste is not just a comic relief figure, like Sir Andrew; he is perceptive when others are not, as Viola notes after the encounter. Feste and Viola actually have a good bit in common; both are paid servants who are much more than they seem to be, and hence present some threat to each other since they search out each others' secrets. Viola knows, unlike Olivia, Orsino, and the others, that Feste is anything but a fool; he "is wise enough to play the fool, and to do that well craves a kind of wit," Viola says of him (III.i.59). Feste is a good judge of human nature, as he shows in his correct assessment of Orsino in Act II; and, he might also be the only one in the play to guess at Viola's disguise.

"Now Jove in his next commodity of hair send thee a beard," Feste says to Viola (l. 44); the statement can be taken as proof that Feste knows that Viola is in disguise, and Viola's quick and somewhat agitated reaction supports this claim. That conclusion, however, is uncertain; though Viola does admit that Feste is more perceptive than most of the people she has come across, and by her estimation, should have the intelligence to be able to see through her disguise."