'Peculiar' originally meant 'one's own' — from Latin 'pecus' (cattle). Private property looked 'odd' to others.
Strange or odd; unusual or distinctive; belonging exclusively to one person or group.
From Latin 'pecūliāris' (one's own, private, special, belonging to oneself alone), from 'pecūlium' (private property, one's own savings, property in cattle), a diminutive of 'pecū' or 'pecus' (cattle, a herd, livestock), from PIE *peḱu- (wealth, movable property, cattle). In ancient Indo-European economies, cattle were the primary measure of wealth — liquid assets that could be moved, exchanged, and accumulated. PIE *peḱu- gives Latin 'pecū' (cattle), 'pecūnia' (money, wealth — originally 'cattle wealth'), 'pecūlium' (private property, saved from cattle), and
'Peculiar,' 'pecuniary' (relating to money), and 'fee' all trace back to PIE *peḱu- (cattle, wealth). In ancient economies, livestock was wealth — so the Latin word for 'private property' literally meant 'one's own cattle,' and strangeness was just the quality of being distinctively yours.