It's our ability to empathize and reason that makes us human. It's true that some species are thought to be able to empathize or reason to some extent... but nowhere near like we, as humans, can. These two traits make us distinctly human.
So...
Morality is subjective to our ability to empathize and reason.
And, obviously, an objective component can complement this... i.e. a code of ethics created by an organization