Paleolithic people made handaxes to show off their sexiness, argue some paleontologists

"Hey baby, check out my sweet biface!"

"It's highly symmetrical! Let's mate!"

— Conversation between two Homo Erectii in western Asia about 1.4 million years ago.

"Why was time invested in making [handaxes] when less extensively retouched artefacts, or even plain unretouched flakes, are suitable for tasks such as butchery, woodworking and the other activities for which handaxes were used?" asked Dr. Marek Kohn and Dr. Steven Mithen in their paper "Handaxes: Products of Sexual Selection?" published in Antiquity 73, 1999.

Their answer: "Teardrop-shaped handaxes were products of sexual selection and as such were integral to the processes of mate choice within socially complex and competitive groups."

Kohn and Mithen's argument is commonly referred to as the "sexy handaxe theory," and paleontologists have been debating it for over 20 years.

Subsequent critiques have focused on different elements of Kohn and Mithen's argument. Most
notable has been the reply (also in Antiquity) by Machin (2008) entitled "Why handaxes are just not
sexy," and focused on the lack of empirical support for the theory (a criticism echoed by Nowell and
Chang 2009). This reply was countered by a response from Mithen entitled "Whatever turns you on"
in which he provocatively concludes "Why does it feel so enthralling to hold a finely made
symmetrical handaxe in ones hand? … My guess is that the thrill of holding a finely made
symmetrical handaxe is an echo of the Stone Age past, of a time when these objects played a key role
in sexual display and to which our modern minds remain attuned" (Mithen 2008: 768). The debate
continued with further discussion by Hodgson (2009) who argued that symmetry could not be
reliably linked to greater genetic "fitness" or attractiveness, and subsequently Hayden and Villeneuve
(2009) arguing for a functional role to symmetry in producing a longer-lasting edge to a bifacial tool.

After a certain point the editor of Antiquity stopped publishing papers about the sexiness of handaxes, but the editors of Palaeoanthropology weren't shy about opening their pages to the attention-grabbing topic and the debate continued over there:

where Nowell and Chang (2009) argued contra Mithen (2008) that sites with apparently large numbers of unused handaxes can accumulate through repeated visits, and that little evidence for use-wear may relate to the particular sedimentological conditions rather than being evidence of concentrated manufacture and discard without use.

One current counter theory is that handaxes don't indicate sexiness as much as trustworthiness (though the two aren't mutually exclusive):

There are several grounds for suggesting that a concern with symmetry and with conformity to the
golden ratio in handaxe form functioned as a signal of collaborative potential in Acheulian societies.
The emotional capacities expressed in handaxe form, the role of such capacities in reciprocal
altruism in higher primates, a greater significance in modern hunter-gatherers and the match
between appearance of handaxes and particular social contexts support the argument that such
artefacts signalled "trustworthiness" to others.