Why do people think their lives should mean something?

Because they have goals and purposes that are inherently meaningful. So their lives point to the goals they seek. A life that points to something meaningful is imbued with the meaning of that thing, People are mostly used as tools for somebody else’s purposes but they do not admit to that. They claim to have their own purposes. They want their lives to mean something, and that desire itself has meaning. The idea of Camus — nothing means anything is true in respect to objective physical Nature, but not true in respect to the mind of Victor Frankl, or your mind, or mine.