I asked this very question at the Game Fair several years ago, both at the BDS and BASC, neither had an answer both said to the effect that this is how they have always been known, go away and don't ask such silly questions again.
best of luck in your quest,
It all goes back to the old language of the hunt - red deer were considered superior, the rest were 'lesser species' (in fact the roe had no real status at all, as it didn't provide a good run for the hounds). Hence 'stag' and 'hind' for red, 'buck' and doe' for fallow to differentiate the species.
Sika, being closely related to red deer, seem to have taken on stag & hind by default.