Lets try to make sense of the answer to this question.
Around the turn of the 17th century 3 stallions were brought to England, from the middle east, to breed with native mares to produce horses capable of being outstanding racers. Those 3 stallions were Byerly Turk, Darley Arabian and Godo;phin Arabian, imported by their respective owners Captain Robert Byerly, Thomas Darley and Lord Godolphin.
These 3 stallions sired, amongst others, the 3 horses that
became the sires of all British and American thoroughbred racehorses. These 3 were Eclipse, Matchem and Herod.
The original 3 (Byerly, Darley and Godolphin) obviously had sires too; so who knows where the bloodline actually started; probably in Noah's Ark.
So ... Eclipse, Matchem and Herod were the starters of the thoroughbred bloodline of horses specifically bred for racing in the UK and USA, although we also know who their fathers were; i.e. Byerly, Darley and Godolphin.
For easy keeping of the Stud Book one offspring of each of the original imported horses was chosen to represent the start of the line. These were; from Byerly Turk - Herod; from Darley Arabian - Eclipse; and from Godolphin - Matchem.
So now you can choose which you believe to be the answer and then find someone to argue with for a l o n g l o n g time.