Why does Ciel phantomhive wear an eyepatch?

Answer 1

Lavi already stated in the reverse novel's that the eyepatch was not due to an injury.

Although he was hit by a stray bullet, the earlier statement contradicts the main theory.

The section where people talk about what Bookman said, that was to do with his hair that lavi pulled out due to the pain.

The more plausible and canon theory for Lavi's eyepatch is to do with his role as a Bookman and his memory.

Answer 2

He wers one because under it is his other colored eye that has the symbol of a human and demon making a contract. Ciel made a contract with the demon Subastian and that's how his eye has that symbol.