The answer to the question in the title is, of course, a resounding "Hell no!".
Despite what you may have been taught, centaurs are not creatures of fable or mythology. Neither did the race die out entirely when their mares left them to wander off and die lonely deaths on the plains of Central Asia.
The story of how the species was saved and survived to this day through heroic efforts by the first laird and his wife is a living legend within clan McMillan.
The first laird Callum and his spouse the goddess-witch Minerva came across the last three living centaurs during their travels in Asia Minor. They were in a pitiful state after a long life of ribaldry, whoring and worse.
With the skilled ministrations of Minerva, the centaurs were brought back to health and were offered a safe haven in the laird's clan, who at the time lived in the Scottish Highlands.
Over time there was intermarriage between the species and the McMillan clan became the renowned shapeshifters they are today. (Clan McMillan and their distant relations the Ashdene family are among the last remaining shapeshifters still among us.) To this day they choose at will in which manner they wish to present themselves.
Notes:
Centaur body (Bento) and skin from Jinx. https://marketplace.secondlife.com/stores/52351 (right now only sold at We ♥ Roleplay (SLurl)) UPDATE: Landmark to the New Jinx Store (SLurl)
The armor is my Valentine's Day gift from my husband Tomais.