Emotivism is the non-cognitive view that moral statements are statements of sentiment or emotional preference so that, for example, the statement “killing is bad” means “boo to killing,” and “killing is good” means “hooray for killing.” Thus, according to emotivism moral statements are non-cognitive because they are reducible to statements such as these, which are neither true nor false.
As a general rule, it is safe to say that most moral statements are intended to convey something more than an emotional preference among alternatives, though it is also safe to say that some people intend moral statements to convey nothing more than their own emotional preferences among alternatives. To make it personal, when I make moral statements, I only ever intend them to convey my emotional preferences among alternatives.
The problem with emotivism is that it holds that moral statements are mere statements of emotional preference even if those who make such moral statements explicitly claim their statements are not intended to express mere emotion or sentiment but actual truths or immutable laws discoverable by human beings. I would prefer to deal with claims that moral statements reflect actual truths or laws of the universe on their own terms rather than simply dismissing such possibilities out of hand and treating such statements as rooted in emotional or sentimental preferences, for the simple reason that many (and very likely most) people do not intend moral statements to only express sentiments. Of course, as is apparent from my earlier arguments, my view is that insofar as moral statements are intended to express truths about the universe or reflect laws discoverable by human beings, they are all false or at least impossible to verify. Insofar as emotivists make this claim, I agree with them, but insofar as they seek to gloss over the fact that moral statements are ordinarily intended to convey truths or reflect laws discoverable by people, I find their approach incomplete.
While admittedly most people making moral statements intend them to refer to factual states of affairs, it is possible for a person making a moral statement to intend that statement as a pure statement of sentiment or emotional preference independent of any factual state of affairs. When a moral statement is intended in this latter way, emotivism is a valid meta-ethical theory, but not otherwise.