Because L.A. Unified was afraid of secessionists.
In 1947, Torrance broke away from LAUSD to form its own school district. When it left, it took Torrance High with it. (It's an attractive piece of property, most famous as West Beverly High in "Beverly Hills 90210.")
In response, LAUSD issued a policy that no new high schools would be built outside the Los Angeles city limits.
That way, if any other cities decided to break away, they would have to build their own schools.
Gardena High was built in 1956. The site, at Normandie Avenue and 182nd Street, was in unincorporated land that was annexed into the city of Los Angeles. But the school was surrounded on all sides by Gardena, and it served Gardena students. (The same decade, LAUSD built Narbonne High in Harbor City to serve students in Lomita.)
The fear of secession was (mostly) unfounded. Gardena leaders have contemplated withdrawing from LAUSD a couple times over the years, but it has never gone beyond talk. Meanwhile, the LAUSD policy has long since been overturned.
Thanks to Don Dear, former mayor of Gardena and Gardena High alum.