Material and behavioural elements associated with the term Neolithic are almost completely absent in Australia. Among the few exceptions are the domesticated dog (originating in the Near East and reaching Australia by 3,500 years ago as the dingo), together with limited evidence for permanent settlements, food storage, long-distance trade and manipulation of wild resources in some areas. While it has been suggested that the latter developments represent independent local trends toward more complex societies that might have led to an Australian Neolithic if not for the arrival of Europeans, the Neolithic is essentially conspicuous by its absence. Particularly striking is the absence of agricultural practices, despite recent claims to the contrary. Also not present is another one of the original (though generally over-looked) defining attributes of the Neolithic: the weaving of textile fibres for clothing. Claims for indigenous Australian agriculture are reviewed here, and the few purported cases are found to be weak. An unconventional model for the transition to agriculture is presented, advocating a significant formative role for clothing, specifically textiles. This suggests that a typical absence of clothing (and total absence of textile clothing) provides a clue as to why agriculture did not develop in Australia.