Alvy hates L.A. To him, the City of Angels represents all that's wrong with the world. In fact, when Rob suggests relocating to Hollywood, Alvy says:
ALVY: I don't want to move to a city where the only cultural advantage is being able to make a right turn on a red light.
Hey, Alvy: What about Oki Dogs, Venice Beach, and, you know, the film industry?
But Alvy's not buying it. For him, Los Angeles is the epicenter of superficiality. When he actually does go out west, he gets physically ill and has to cancel his television appearance.
Here's the thing, though: Alvy doesn't just loathe L.A. because he finds it fake. He dislikes it because it symbolizes Annie's freedom. When she moves out there to pursue singing professionally, she leaves Alvy behind. She doesn't involve him in the decision to go because she doesn't need to. It's a big, exciting change in her life, and Alvy? He's incapable of change. She tells him point blank:
ANNIE: […] You're like New York City. You're just this person. You're like this island unto yourself.
When Annie abandons New York for Los Angeles to kick-start her career, Alvy takes it as a personal rejection and, boy, does it smart. Luckily, he's got an entire city of angry people to feel bitter around—maybe he can go yell at a rando in the subway for manspreading?