Moral Non-Cognitivism
Non-Cognitivsm is the the claim that moral expressions are not "truth apt" because they are not intended to express claims of fact that can be true or false -- and by extension, moral knowledge is impossible.
For a non-cognitivist, a moral expression such as "Murder is evil" is comparable to an expression like "Murder blegh!" (Emotivism) or a command like "Do not murder.", and according to a non-cognitivist such expressions can not be true or false.
Non-Truth-Apt Expressions
Emotional Expression
Even if the non-cognitivist claim that "Murder is evil" is comparable to "Murder blegh!", the fact is that "Murder blegh!" still remains comparable to another fact claim: "I dislike murder." This fact claim DOES have truth value -- the person could be sincere, lying, or perhaps in denial his or herself. While the truth value of these claims may be something difficult to determine, a person's personal attitudes about something remain a matter of empirical fact and knowledge. Equating morality to personal belief might be a form of radical subjectivism or egoism, but it's not non-cognitive.
Commands
Like emotional expressions, commands also carry truth value. If "Murder is evil" is comparable to "Do not murder", the latter is also comparable to either a claim of desire "I don't want you to murder" which has truth value, or an external empirical claim of consequence "Do not murder or else" Where "or else" indicates "I will do something to you that you don't want to happen/something you don't want to happen will happen to you" which also has truth value.
The way non-cognitivists obfuscate the fact of these implicit truth claims is by "translating" the moral statements very conveniently to a half-way point where the truth claim is not explicit or is unclear. The attempt to have it both ways -- having the liberty to impose interpretation on other's claims and reduce them as you see fit but denying further reduction -- is innately intellectually dishonest. There's no objective metric by which we could reason moral claims to mean whatever non-cognitivists half-interpret them into but not their final implications; which are all truth-apt.
Semantic Intention
Even if it were the case that there were non-truth-apt expressions that don't easily reduce into obviously truth-apt ones, there's no reason to believe that people intend their moral expressions not to be truth apt. If you ask people whether the moral claims they're making can be true or false, they'll say yes (and that they are true). Aside from intentional sarcastic claims (e.g. "mayonnaise is evil" due to personal dislike of mayo), if you ask people whether sincere moral expressions are meant to only convey personal opinion most people will answer no -- that is not their intent in making those expressions. Likewise, if you ask people whether when making moral expressions they are merely telling other people what to do, again people will answer no -- they may answer that people should do/not do those things, but that it's not a command (Divine command theorists may say a god has commanded this, but that is again a truth claim about an external fact).
The fundamental problem with non-cognitivism is that it doesn't listen to people when they clarify what they intend to convey with moral claims. While a person's belief about the shape of the Earth may not be relevant to the physical fact, a person's belief about what he or she intends IS a primary source and is very good evidence for that intent. Non-cognitivsts must thus either incredibly uncharitable to believe people are lying about what they intend to express, or believe that people are so stupid they don't even have any idea what they're trying to say -- including many of the most educated philosophers and theologians in the world. In this case, according to non-cognitivists, only non-cognitivists have magical insight into people's true intent in making moral statements, which also makes the theory of non-cognitivism fundamentally unfalsifiable making the theory intellectually dishonest to its core. For a more intellectually honest rejection of moral realism which doesn't claim people are either dishonest or that people don't even know if they're trying to make claims or not, see Moral Error Theory, or see Minimal Moral Realism for an alternative to the stronger claims of Robust Moral Realism (which is what anti-realist positions are usually construed to challenge).
