Trying to term morality "objective" or "subjective" has always seemed stupid to me and very confused. The word objective as used here doesn't even make sense. If by "objective morality" you mean "moral truths independent of any mind's beliefs about them" that doesn't really work. After all, one still has to accept some particular ethical framework as the most suitable one even if you take this meta-ethical view (which is called "moral realism" by the way).
The problem is that moral statements are normative statements, close siblings to statements like "Chess is better than checkers"; they entail value judgements, which have a different logical standing. That itself certainly doesn't negate the possibility of moral realism being true but it does, I think, clue one in on how not to argue for it.
The problem is that moral statements are normative statements, close siblings to statements like "Chess is better than checkers"; they entail value judgements, which have a different logical standing. That itself certainly doesn't negate the possibility of moral realism being true but it does, I think, clue one in on how not to argue for it.