Moral objectivism is the view that there are moral truths that apply to everyone, whether they agree with them or not – just as there are truths about physics or geology or mathematics.
One argument commonly used against moral objectivism is that people often disagree about ethical matters. By itself, however, this isn't a very strong argument. After all, there are disagreements in every area. For instance, some people believe the earth was created less than 10,000 years ago, others that it formed more than 4 billion years ago – but in spite of that, the age of our planet is a perfectly objective matter. Mere disagreement, then, does not mean anything.
But there is a different argument along the same lines that makes a much stronger case. At the very least, it shows that there is something odd about moral objectivism.
The argument begins with the observation that in other areas, there are facts that are obvious, and that as a result just about everyone agrees with. For instance, everyone agrees that fire is hot, or that 1+1=2. Where there are disagreements, it is because the matter is not regarded as something really obvious.
In ethics, however, that's not the case: there are many things that are regarded as obvious by many – even by most people – but which nevertheless are denied by large numbers of other people. For example, the principle that killing an innocent person is (almost always) wrong is one that, for those who agree with it, seems perfectly obvious – about as obvious as that fire is hot or that 1+1=2. And yet, plenty of people disagree with this principle.
Mere disagreement might not mean anything; but disagreement over what is supposedly obvious is much harder to explain. Why is it just about no one doubts simple truths in arithmetic or simple empirical truths, but so many doubt what – given that they are regarded as equally obvious – should be simple truths in ethics? Might it be because they are not actually truths?
(For more on objectivism and subjectivism in ethics – and why subjectivism is compatible with taking morality seriously – see chapter 5 of my book The Truth about God.)