The idea is that if something is the sort of thing where, if there is a difference, someone has to be right and the other side has to be wrong, you've got objectivity. There is a truth independent of the preferences and opinions of people. So if I say the earth is flat and you say it's round, it isn't just flat for me and round for you, I've got it wrong. If I say "Coke is better than Pepsi" and you disagree, we can both be right for ourselves, and can remain right even if I take the Pepsi challenge and remain a Coke drinker.
What about ethics? Is it more like the Coke case or like the flat earth case? With highly vexed issues like abortion, we are tempted to think it is like the Coke case. If we contemplate inviting someone over for dinner and then cooking them as dinner, relativism or subjectivism is hard to maintain. Is my disagreement with Hannibal Lecter on what is morally appropriate to cook and eat a mere matter of taste (pun intended)?