Meaning is a mental construction. For it to exist in the universe, it requires a meaning-maker who has a mind that can construct meaning. Meaning cannot exist by itself. It needs a mind.
The mind of a meaning-maker, including all its contents, does not share the same metaphysical status of objective physical things. They have an entirely different metaphysical status. They are concepts.
Mental constructions are not objective. Therefore, they are subjective. And because meaning is a mental construction, it too is subjective.