What is up with this cat?

My friend's cat, Bruce, is about a year old and neutered. Your first impression is of a very loveable, cuddly cat, as when you first arrive at the house, he walks right up to you, rubs against you, rolls around on the floor inviting you to pet him, walks across your lap, all kinds of lovey cat things. But the moment you wrap your arms around him or try to pick him up, he gets pissed. He growls and hisses, and if you try and pet him, he bites you. Then, you put him down, and he goes back to his lovey self. Neither my friend nor I can figure out why he does this. He started doing it out of nowhere when he was about six months old. She's taken him to the vet, who can find nothing wrong with him.