For anyone who knows how to draw, it's not that difficult to draw a moderately realistic person, or animal, or object. So why is there no ancient artwork that looks accurate? Ancient greek, egyptian, japanese, chinese, african, and other artwork is all very stylized and cartoonish (poor word choice, but you know what I mean). As far as I know, it wasn't really until the European Renaissance that artwork that really looked realistic came about.
Generally speaking, both ancient Greece and Rome knew periods when artists strove for accurate and candid depictions of people and objects. Hellenistic art (around 320 B.C. to 30 B.C.) has some aspects of idealization when compared to today's standards, and the emotionalism of some well-known examples like the sculpture of Laocoon is quite different then what we would expect of a realistic depiction of the same scene today.
Nevertheless, the portrait sculptures of this era don't lack realism as far as proportions, the positioning of limbs or the accuracy of details (e.g. embellishments of clothes, hairstyles) are concerned. Rather, hellenistic artists chose models who showcased the ideals and standards of beauty of their time - youth, slim/athletic bodies, long wavy hair and so on. For some examples of hellenistic sculpture see e. g. the picture gallery of the Classical Art Research Centre Oxford.
Late Roman republican portraiture (mostly during the 1st century B.C.) is especially known for its verism, i. e. a tendency to include unflattering features for the sake of greater realism. Portraits of this period openly show signs of age, such as wrinkles and baldness, and they don't try to hide the plain facial features of the depicted individuals - e. g. in this bust of a woman from the collection of the Michael C. Carlos Museum at Emory University.
Greek and Roman writers also emphasized the importance of verisimilitude in art and used realism as a criterion to judge the quality of an artwork: The Posidippus papyrus, a poetry book from the third century B.C., contains some epigrams on bronze statues that focus strongly on realism. Philostratos the Elder ( c. 190 – c. 230 AD) claimed that a bee in a painting of Narcissus was depicted in such a way that he could not decide whether it was in fact part of the artwork or a real insect that felt drawn to the painted flowers by mistake. (Philostratus, Imagines 1.23.2)
Sources:
Fejfer, J. (2008). Roman portraits in context (Vol. 2). Walter de Gruyter;
Elsner, J. (2007). Roman eyes: visuality & subjectivity in art & text. Princeton University Press;
Williams, M. F. (2005). The New Posidippus: Realism in Hellenistic Sculpture, Lysippus, and Aristotle’s Aesthetic Theory (P. Mil. Vogl. VIII. 309, Pos. X. 7–XI. 19 Bastianini= 62–70 AB). Leeds International Classical Studies, 4, 1-29.
