"Haole"[,] some Hawaiians believe[,] is a sort of antonym of "aloha"[.] "Haole" is a word predating Western contact and can be used to describe nonnative plants and animals as well as people. Still, there's a popular myth that the derivation comes from the phrase for "without breath," ha being the word for breath. (As in "aloha," which can be used as a greeting or a farewell or to indicate love but literally means "the presence of breath" or "the breath of life.") This "without breath" interpretation of the word "haole" was supposedly applied to Western visitors because they refused to engage in the traditional Polynesian greeting in which two people touch noses and embrace while breathing each other in.
Breath is considered sacred in some cultures. I'm reminded of Joseph Campbell's discussion of the Hebrew word for God, which can be written YHWH; Campbell noted the resemblance of the name of God to that of an inbreath and outbreath.
In typing the quote I remembered that the "Western visitors" Sarah Vowell is talking about came to Hawaii from the East. White people came to the Americas from the East, too. In that sense all Europeans are Easterners to the New World and Polynesia. Europeans became "Westerners" by virtue of being West of China and India, the two civilizations greater than all of Europe after the collapse of Rome, at least until Europe discovered the New World and began to feed on it.
source: Unfamiliar Fishes by Sarah Vowell