Emotivism describes a system of ethics and moral philosophy that regards ethical judgements as expressions of emotions, attitudes, and feelings, rather than objective assertions. For emotivists, moral statements do not appeal to objective facts, but are relative in nature. Rather than expressing a truth claim, they describe an emotional state.
One way to critique emotivism is to find philosophical alternatives to its central claims. The dominant paradigm within liberal political theory treats human emotion with suspicion. This can be traced back to Descartes, who went to great lengths to parse the difference between mind and body. Descartes's famous maxim "I think, therefore I am" describes his mistrust in the bodily emotions in favor of the certainty that comes with reason. This school of thought came to be known as rationalism and included the likes of Thomas Hobbes and Spinoza.
For MacIntyre, the Enlightenment failed in its quest for a universal solution to the human condition and, in doing so, promoted a form of reason responsible for the contemporary social milieu. He wants to seek out theories that don't attempt a final, ultimate solution or make claims to absolute certainty. MacIntyre's indictment of the Enlightenment paints a broad brush over a constellation of thinkers with quite different views. To counter MacIntyre, one might argue that the Enlightenment made some positive improvements to our political culture by promoting transparent public discourse, and above all, the idea that humans deserve to be the authors of their own decisions.
MacIntyre believes he is avoiding the emotivism in thinkers such as Sartre and Nietzsche by returning moral philosophy to Aristotle and Aquinas, for whom he thinks hold out for a moral rationality reluctant to claim universality.