There are some occupations in which it is impossible for a man to be virtuous. — Aristotle (384–322 B.C.)
To which occupations was he referring?
According to Aristotle, legitimate trade consisted of providing needs essential for the "good life." Barter was an acceptable means of trade, but profit making seemed absurd. Aristotle held that those who sought a profit were despicable characters lacking in proper virtues. After all, one who made a profit had only two options, to hoard the money or to spend it on excessive wants and desires. Thus, to Aristotle, this line of work seemed to be unvirtuous and even despicable. (Denis Collins, 'Aristotle and Business', Journal of Business Ethics, Vol. 6, No. 7 (Oct., 1987), pp. 567-572: 572.
To spell this out in more detail (references are to Aristotle's Politics except for 'EN' = Nicomachean Ethics):
Aristotle introduces money as a development of exchange, and he sees this as evolving through four forms. The first (i) is barter or the exchange of commodities without money (1257al5-30), which we can represent as C-C. Barter is inconvenient because the acts of sale and purchase are fused into a single act. Money came into existence in the first place, he says, in order to make this sort of exchange easier (1258b4-5), by allowing the sale (C-M) and the purchase (M-C) to be separated in time and place (EN., V, 1133bl0f). This gives (ii) the second form of exchange, natural chrematistike (1257a30-41), which may be represented as C-M/M-C, or for short C- M-C. Once people have become accustomed to this, Aristotle says, another form of exchange arises, (iii) unnatural chrematistike, in which people can come to market, not with surplus goods they have made or grown which they want to exchange for things they need, but with money. Their aim is to get money by buying goods and selling them for a greater sum (1 257b 1-40); it can be represented as M-C/C-M, or M-C-M for short. This is justly discredited, he says, because it involves 'people taking things from one another' (1258blf). (iv) The fourth form is usury (obolostatike), the lending of money at interest, M-M, or 'the breeding of money from money', which he says is the most hated sort and with reason (1258b 1-8). (Scott Meikle, 'Aristotle on Money', Phronesis, Vol. 39, No. 1 (1994), pp. 26-44: 26-7.)
Aristotle and banausia [manual labour]
[I]n the De Philosophia of his transitional phase, where he gives the name of wisdom (sophia) to each of the five stages he distinguishes in the growth of civilization: first, the introduction of work and of the techniques required to satisfy the most pressing needs of ordinary life; second, the introduction of the arts of refinement and elegance; then, the creation of laws, the study of nature, and finally, the contemplation of the first cause. Labour and technical skills, then, are already held to be sophia. Later, in the first chapter of the Metaphysics, Aristotle expresses this concept more clearly, distinguishing two elements in labour: the invention and supervision of the technique; and its actual execution. He considers those who direct the work to be more gifted than those who merely carry it out mechanically, never stopping to think of the reason for what they do. (Rodolfo Mondolfo and D. S. Duncan, 'The Greek Attitude to Manual Labour', Past & Present, No. 6 (Nov., 1954), pp. 1-5: 4.)
Such 'mechanical work', of which those who do it never stop 'to think of the reason for what they do', stymies the development of virtue. Some remarks of Julia Annas are helpful here:
Humans are equipped by mere nature to develop virtue, but do not do so unless habit is directed by reason to produce a rational direction of one's life and employment of external goods. In the context of the Politics we also need to remember the thesis that humans are by nature politika (πολιτικά) - social and political beings. For it is only when habit is directed by reason to produce dispositions to engage socially, culturally, and politically with others in a form of society (one which Aristotle identifies with the polis) that humans achieve the goal of natural development. (Julia Annas, 'Aristotle's "Politics": A Symposium: Aristotle on Human Nature and Political Virtue', The Review of Metaphysics, Vol. 49, No. 4 (Jun., 1996), pp. 731-753: 736-7.
Aristotle assumes that, for the manual worker, habit cannot be directed by reason to produce a rational direction of one's life and employment of external goods. The conditions of life of the banausos, the class of manual labourers, is such that this class has neither the leisure, the education, nor the command of external goods to acquire the ethical and intellectual virtues outlined in the Nicomachean Ethics, III-VI.
Not exactly what Aristotle says ...
Politics,1278a : As there are several forms of constitution, it follows that there are several kinds of citizen, and especially of the citizen in a subject position; hence under one form of constitution citizenship will necessarily extend to the artisan and the hired laborer, while under other forms this is impossible, for instance in any constitution that is of the form entitled aristocratic and in which the honors are bestowed according to goodness and to merit, since a person living a life of manual toil or as a hired laborer cannot practise the pursuits in which goodness is exercised [emphasis added].
An alternative translation of the sentence is :
"it is impossible to pursue the things of virtue when one lives the life of a vulgar person or a laborer".