Brideshead is an unusual and unique individual with "a gravity and restraint" beyond his years. Anthony describes him as "something archaic, out of a cave that's been sealed for centuries." He doesn’t have Julia or Sebastian’s good looks, in fact "has the face as though an Aztec sculptor had attempted a portrait of Sebastian." He also shares none of Sebastian’s youthful verve nor his ability to charm – Brideshead doesn’t even like to drink!
He also has his own method of thinking, speaking, and understanding things, a method which isolates him from others and makes communication, particularly between Charles and him, nearly impossible. Brideshead seems to recognize this: "It's something in the way my mind works I suppose. I have to turn a thing round and round, like a piece of ivory in a Chinese puzzle, until – click! – it fits into place – but by that time it's upside down to everyone else." And so does Charles, who concludes from their first debate on religion that "this disagreement was not a matter of words only, but expressed a deep and impassable division between us; neither had any understanding of the other, nor ever could."
This proves to be very true, particularly by the end of the novel when Charles is shacked up with Julia and Brideshead is planning to marry an ugly, over-the-hill widow. Brideshead unfortunately applies his own weird brand of logic and concludes that it’s perfectly reasonable to call his sister out for being a sinful strumpet, essentially (our words, not Brideshead’s). Brideshead is so caught up in logic and rules that he doesn’t even comprehend the hurt he caused his sister by saying as much:
"Bridey, what a bloody offensive thing to say to Julia!"
"There was nothing she should object to. I was merely stating a fact well known to her."
OK, so he’s apparently devoid of people skills. (No danger of being charmed to death here.) How did Brideshead get this way? For the umpteenth time, we turn to Cordelia for answers:
"If you haven't a vocation it's no good however much you want to be; and if you have a vocation, you can't get away from it, however much you hate it. Bridey thinks he has a vocation and hasn't. I used to think Sebastian had and hated it – but I don't know now He’s as doomed as Sebastian."
She later says that "there are […] people who can’t quite fit in either to the world or the monastic rule," and it would seem that Brideshead is one of them. He’s obsessed with religion but never became a priest. He was left in the world with essentially nothing to do, and so became a bit of a farce – he ends up collecting matchboxes for a living. Look at what Charles has to say:
He had been completely without action in all his years of adult life; the talk of his going into the army, and into Parliament, and into a monastery, had all come to nothing. […] He was usually preposterous yet seldom quite absurd. He achieved dignity by his remoteness and agelessness; he was still half-child, already half-veteran; there seemed no spark of contemporary life in him; he had a kind of massive rectitude and impermeability, an indifference to the world, which compelled respect. Though we often laughed at him, he was never wholly ridiculous; at times he was even formidable.
It’s clear that Brideshead never becomes an entirely comic figure, probably because he’s too much of a tragedy – and too much a reminder of Sebastian’s own "doomed" predicament.