Owls are considered very magical animals due to their ability to track down the recipient of a letter no matter whether or not there's an address attached to their name. On the other hand, pigs are considered very non-magical because of how difficult they are to charm. A fear/disliking of pigs has traditionally been seen as a sign of pureblood heritage!

It makes me giggle, because muggleborn @"Dionisia Tweedy" is very self-conscious about her non-magical heritage has a piglet patronus