If they've got the bodies of horses, presumably they'll need to eat like horses? But will the human end enjoy eating tons of hay and oats and apples and polos? And the quantity of food through a little human mouth will be an issue. And the there's the poo. If they eat horse food, fine. Horse poo is dry and comes out the bum in dry lump, but if the centaur eats human food, sausage-egg-n-chips etc, the poo will be more human won't it? Bit more splatty and sticky? How will they wipe their bums? Their horse parts are long and their arms won't reach. (In the photos I've seen).
And then there's genitals. They'll need to cover them up, especially the males who'll have enormous winkles. But how do you put trousers on their horse areas? Would they cover the rear end and rear legs? Or would they come up from the ground on the front AND rear legs. And do you go under the tail or over and leave a tail hole? And how will the get them on? It's the little arms again.
I believe they have as much right to exist as the next mythical being, but are we prepared for them in this country?