Some of my hobbies are making me think about fabric. I used to think that fabric containing both cotton and linen was a product of the last thousand years, as cotton production spread west from India into areas with a strong tradition of weaving linen. In the second half of the middle ages, cities in Italy began importing cotton from Egypt and Turkey and Syria and weaving it themselves, and the trade slowly spread north across the Alps. The basic idea was that cotton was cheap and absorbed dye well, while linen was strong but hard to colour. Some weavers found that if they used cotton for the warp threads, they tended to snap. So a mixed cloth with a linen warp and cotton weft was both strong and colourful. In the middle ages these cloths were known by names such as English fustian, Italian fustagno (from the suburb of Fustat in Egypt) or German Barchent. Today weavers are comfortable with a cotton warp, and artificial dyes can colour pure linen any imaginable colour, but cloth with cotton running one way and linen threads the other is still used for shirts and other items. I did not think that these mixed cloths existed before the middle ages. But now read this!
The finds of archaeological linen textiles display a wide range of qualities in ancient Greece. However, they are primarily burial finds and thus no adequate source for the topic of clothing practice. Nothing, however, suggests that linen textiles were rare, or associated only with female burials or those of foreigners. Linen textiles occur much more frequently than wool textiles in the archaeological record in Greece, as Moulherat and Spantidaki have observed, but this only reflects the preservation conditions in Greece, and does not denote a choice of fibre. A linen textile of impressive size came to light in Eleusis: it measures 220 cm × 50 cm. It was found in a bronze vessel dating to the mid-5th century BC. Preserved linen textiles with 100 threads per cm are not unknown in classical Greece. From the 5th century BC such a linen textile was found in a tomb at Kerameikos; another 5th century linen fabric of similar quality comes from Kalyvia Thorikos. In another 5th century Kerameikos grave, linen textiles with remains of stitch holes from embroidery and fabrics decorated with purple were recovered. The original assumption of silk fabrics has now been proven wrong in new analyses by Christina Margariti and colleagues who demonstrated that there are four different fabrics of which two are of made of linen, while another fabric is probably made of cotton, and the last is woven of linen warp and cotton weft.
That quote comes from an article by Marie-Louise Nosch where she argues that scholars have been too hasty in following a passage in Herodotus and dismissing the use of linen in classical Greece (Hdt. 2.105 tr. A.D. Godley):