"All people are a mystery" is ungrammatical because you have a plural subject and a singular complement. One should say "people are a mystery" or "all people are mysteries" or even "every person is a mystery."

Notice the differences among these three. "People are a mystery" means that people as a whole are one big mystery. "All people are mysteries" means that the set of all people is a set of mysteries. "Every person is a mystery" means each individual person is a mystery. For the verb "to be," the last two have equivalent meaning of course.

Compare: "At this school, all boys love girls" with "At this school, every boy loves a girl." The first claims the boys are all heterosexual, but the second claims they're monogamous too.

"All people are a mystery" is ungrammatical because you have a plural subject and a singular complement. One should say "people are a mystery" or "all people are mysteries" or even "every person is a mystery."

Notice the differences between these three. "People are a mystery" means that people as a whole are one big mystery. "All people are mysteries" means that the set of all people is a set of mysteries. "Every person is a mystery" means each individual person is a mystery. For the verb "to be," the last two have equivalent meaning of course.

Compare: "At this school, all boys love girls" with "At this school, every boy loves a girl." The first claims the boys are all heterosexual, but the second claims they're monogamous too.