I don't think anyone denies that the Greeks used the T&Y cuirass - there is plentiful iconographic evidence for that. The problem is what material those depictions dating to after the Archaic period (this debate only really applies to that time, since we know from Homeric literature and early Greek poetry that linen cuirasses were definitely worn by Greeks before the Archaic period) are meant to represent. When people say that the Greeks didn't use the linothorax, they are using the word's ancient meaning (i.e. a linen cuirass), and not its modern meaning (the T&Y cuirass).
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