Neill hailed from a traditional Southern family from Lexington, Missouri. His father had come to Lexington from Lee County, Virginia in the 1830s. Hyman's father, Henry Alexander Neill, practiced law and would have joined the Confederacy when the American Civil War began, however, he decided he could not disavow his oath to support the Constitution and ended up joining the Union. This choice, coupled with his wife's death, caused him to move his family to Warrensburg, Missouri after the war. His date of birth is possibly unknown.