Explain why Aristotle’s virtue ethics would be better than John Mill’s utilitarianism and Kant's views towards making the world a better place.
What makes Kant an important Enlightenment thinker is his moral and political philosophy, together with his deep sympathy with all the tendencies: toward individual freedom. ("Kant: Self-Determination in the Age of Reason." Frostburg University)
Kant's contribution wasn't so much toward "making the world a better place"--this was the preserve of the French philosophers like Descartes and Locke and Diderot who designed projects for increasing arable land with swamp drainage and building road construction and improving canal infrastructures--as it was to developing a moral and political philosophy.
Enlightenment is man's release from his self-incurred tutelage. ... [which results in] resolution and courage to use [individual reason] without direction from another. ... "Have courage to use your own reason!" (Kant, "What is Enlightenment?" 1784)
Kant asserts that release from the dominion of the prescribed perspectives and conceptualizations of authority, of society, and of culture leaves an individual free to think for themselves even if it leads to discord with society's prescribed thoughts. The freedom to think independently allows the individual to formulate moral imperatives that construct moral values and virtue for self and society based on what seems universally true regardless of cultural or societal differences.
Our moral faculty, ... general principles of moral judgments ... is a branch of our reason, ... and must be looked to for the abstract doctrines of morality, not ... the concrete [applications]. .... Whatever can be proved to be good, must be so by being shown to be a means to something admitted to be good without proof. ... There is a larger meaning of the word proof, in ... disputed questions of philosophy. ... within the cognisance of the rational faculty ... [which is] capable of determining ... to give or withhold its assent to [a] doctrine; and this is equivalent to proof. (Mill, "Utilitarianism")
Mill's greatest contribution constitutes a duality. The first part is that abstract notions of "good" are to be proved in relation to the derived end result in something that is already acknowledged to be good. The second part relates to happiness and is that (1) happiness is to be sought in that which produces, as far as is reasonable (significant qualifier), the greatest collective good for all "sentient beings" and that (2) happiness has higher and lesser levels. According to Mill, intellectual and moral pleasures are the higher level while physical pleasures are the lower level.
to what degree and how seriously a man must err to be blamed is not easy to define on principle. ... such questions of degree depend on particular circumstances, ... (Nichomachean Ethics)
everybody who understands ... avoids alike excess and deficiency; he seeks and chooses the mean, not the absolute mean, but the mean considered relatively to ourselves (Virtue Ethics)
Aristotle defines "virtue" arete as excellence, specifically excellence in fulfillment of a particular function. He defines "happiness" eudaimonia as well-being from excellence: a sense of well-being, resulting from achieving excellence in the fulfillment of one's functions (Charles Ess Ph.D. Drury University). Aristotle argues that since virtue is difficult to measure in that a person may commit a little error or a great error, each act must be measured by its relevant, possibly mitigating circumstances. He further asserts that, in attaining virtuous conduct, a person must avoid excess in either extreme and choose the relative mean--relative to themselves--being that which is neither too little nor too much for optimum benefit to a specific individual.
In order to argue that Aristotle's virtue ethics is superior to Mill's happiness utilitarianism and to Kant's release from "self-incurred tutelage," which leaves a thinking person free to initiate the moral imperative, one might assert that Mill's definitions are even more ambiguous than Aristotle's and that Kant's methodology is far more complex than Aristotle's instruction about the relative mean. Thus the argument might stand on the (1) difficulty of defining moral concepts of virtue and good and on (2) the simplicity of Aristotle's methodology instructing choosing the relative mean.
These assertions might be difficult to prove. This demonstrates the truth of Mill's assertion that moral good and virtue cannot be proved in relation to themselves but must be proved in relation to their being the means to a good and a virtue that is already acknowledged to be good and virtuous. This proof would be needed notwithstanding that today virtue and moral good are even more difficult to define since there is no firm understanding of good in relation to even music or art and certainly not in relation to virtue.
You would also need to prove that Aristotle's emphasis on the individual is superior to the Mill's and Kant's emphases on the individual's impact on, relationship to, and obligation toward constructing a moral and virtuous society.