A writer-in-residence at a girls' college, Buddy is the second-oldest Glass child and the somewhat hidden narrator of "Zooey." He admits his first-person self only during the brief and cryptic introduction to the story. Other than that, we learn of Buddy through his letter, his third-person narration, and in Zooey and Franny's dialogue.
Buddy is one of the two "bastards," in Zooey's opinion, responsible for the Franny and Zooey's childhood education (Zooey.5.54). He and Seymour, who shared a room and were very close brothers, took it upon themselves to teach their younger siblings religion and philosophy before introducing them to the pursuit of knowledge. In Buddy and Seymour's mind, this is the only way to go.
Like Zooey, Buddy takes on a sort of spiritual guru role in this novel. His letter to Zooey instructs and advises rather explicitly; Buddy doesn't hold back telling his younger brother to act, when and where he wants to, "with all [his] might" (Zooey.3.9). There are also a few Zen kōans to be found in this letter (a kōan is a sort of spiritual riddle meant to be understood through meditation and reflection).
Consider the story of the girl in the supermarket or the pint of pus on the plane. More important than Buddy's advice or stories are his observations, which not only tell us what we want to know about Zooey, but help (or helped, since this letter is four-years-old) Zooey to understand himself. Check out several of Buddy's key observations:
"You worry hell out of me, Zooey. […] I know how much you demand from a thing, you little bastard. And I've had the hellish experience of sitting next to you at the theatre. I can so clearly see you demanding something from the performing arts that just isn't residual there. For heaven's sake, be careful." (Zooey.3.5)
"Waker once said […] you were the only one who was bitter about S.'s suicide and the only one who really forgave him for it. The rest of us, he said, were outwardly unbitter and inwardly unforgiving. That may be truer than true." (Zooey.3.8)
"Seymour said cleverness was my permanent affliction, my wooden leg. […] As one limping man to another, old Zooey, let's be courteous and kind to each other." (Zooey.3.10).
Buddy, we see, is similar to Zooey in his incisiveness and even in his style – he shares his brother's playful, daring use of language. His letter also maintains the Glass family tendency of providing long lectures in the place of conversation. Buddy plays a "spiritual guide" role in resolving Franny's crisis similar to that of Seymour, who is also absent from the plot (see "Character Roles" for a full discussion).
As we mentioned earlier, Buddy provides a number of thought provoking kōans. An interesting one to tackle might be his claim that a man should be able to lie bleeding to death at the bottom of a hill and still lift himself up to watch a woman carry a balanced jug of water safely over its crest. We'll leave that one to you, and instead we'll tackle Buddy's claim at the start of "Zooey" regarding the nature of his tale:
"He [Zooey] feels that the plot hinges on mysticism, or religious mystification. […] I say that my current offering isn't a mystical story, or a religiously mystifying story, at all. I say it's a compound, or multiple, love story, pure and complicated." (Zooey.1.2).
This is a confusing comment, and Salinger's story doesn't point to any one interpretation. One possible way to go is to consider the ending of Franny and Zooey, when Zooey explains to his sister that while she's looking for spirituality in the extremes of Eastern mysticism, it's actually right here in front of her – in Bessie's soup. We can think of Bessie's soup as consecrated, because of the love with which she makes it. Similarly, we can imagine that the spot on the rug where Zooey kept his rabbit is holy because of the way he felt about his rabbits. In this way, Franny and Zooey isn't about religious philosophy – it's about everyday ordinary love.
It's also possible that there is no logical explanation to this riddle of sorts; perhaps we're supposed to understand Buddy's comments as an example of the "no-knowledge" he talks about in his letter to Zooey – as something that can be understood spiritually but not intellectually. We wouldn't put it past that Buddy Glass, that's for sure.