Words like "subjective" and "relative" are tricky. They tend to imply "arbitrary", even though they shouldn't, and they're redundant besides: What in our experience of life isn't subjective? Our subjectivity just is our experience.

Morality is an emotional faculty of human nature, created by a blind and aimless selection process. Moral claims are thus only capable of being true or false insofar as they describe human nature. The rest of the universe doesn't have moral opinions, any more than it has opinions about baseball. (Human nature is not the same as "the human will" -- as Marx put it, man makes his own history, but he does not make it just as he pleases. We can't will our moral feelings, at least not very successfully.)