The Minotaur was a lone creature, the first and only of it's kind. The unfortunate result of a Greek God loosing his temper.
Shortly after King Minos (or Minos The King) ascended to the throne of the island of Crete, he began to pray to Poseidon for a sign of his right to sit on said throne.
Poseidon sent a snow-white bull, the Cretan Bull, out of the sea as a gift to Minos and as proof that he was indeed worthy to be king, and in turn Minos promised he would sacrifice the bull in Posidean's name.
Unfortuanlty, Minos' wife Pasiphaë, took a liking to the bull and begged Minos to spare it. Minos did, and sacrificed a different bull in it's place.
Unfortuatly again, Poseidon was not easily deceived and when he learned of Minos' treachery, he promptly cursed Pasiphaë with zoophilia...
It get's creepy from here on...
Pasiphaë's zoophilic urges got the better of her but alas, she could not seduce the Cretan Bull. So she had a wooden bull built. Apparently a very realistic and attractive wooden bull. And proceeded to climb inside and wait for nature to take it's course. Sure enough this did the trick and soon the palace was blessed with the pitter-patter of cloven feet.
The Minotaur, which they named Asterius, was an abomination. So with the help of Daedalus, The Labyrinth was constructed. As Daedalus puts it, it was a :
chamber that with its tangled windings perplexed the outward way
Minos placed Asterius in the centre, and as he didn't want anyone to know about his odd step-son, he threw Daedalus and his son Icarus in too, but they escaped.
And so the poor Minotaur languished in The Labyrinth alone, for the rest of his miserable days.
...until Theseus paid him a visit.