Why did los angeles overtake san francisco as california's major city in the 1920s?

Because of the movie industry. American films used to be shot on the east coast but lighting and weather was always a problem. Back then they didn't have the sophisticated studio lighting we have today so most well lit scenes were shot outdoors, but on the east coast they often encountered gray, rainy or snowy days which hindered production and lost money for the studio. So the filmmakers moved their projects to LA for the great weather and sunshine. The film industry took off like a wildfire and was a major catalyst (if not THE major catalyst) for the growth of LA.