Benjamin Arbogast was born on November 13, 1825 in Pocahontas, Virginia the youngest of the nine children of farmers Benjamin and Francis Ann Mullins Arbogast. He had early schooling locally but then worked his family's land and served as a local constable. For whatever reason, he determined later to resume his education and after some preparation entered the class of 1854 at Dickinson College in Carlisle, Pennsylvania in September 1850 at the age of twenty-five. Over six foot tall and with the look of the farmer, he became a popular student with undergraduates and faculty, joined the Union Philosophical Society, and fought his way to be at the head of his class when it graduated.
Immediately following graduation, he was engaged for two years as a tutor at Dickinson. In 1858 he joined the Baltimore Conference as a Methodist clergyman and then became instructor of Natural Science at the Dickinson Williamsport Seminary, succeeding his classmate, James Rusling in that position. He left this post almost immediately, though, to take up the presidency of the Wesleyan Female College in Staunton, Virginia. This place had previously been filled by a Dickinsonian; James McCauley, class of 1847, and a future Dickinson president, had served there between 1851 and 1853. In 1860, Arbogast moved on to the post of principal of Cassville Female College in Cassville, Georgia. He remained there during the Civil War. The conflict saw several large skirmishes take place in the area as well as, disastrously, the burning of the college by Union forces under General Sherman in November 1864. Arbogast lost of all his books and possessions in the fire and, according to family lore, was held in a Union prison for a time. In 1866, he and his young family were able to secure another desperately needed position, this time as president of Martha Washington College in Abingdon, Virginia. He remained there for six years. In 1872, he was named as president of Kentucky Wesleyan University but moved on in 1874 to head the Valley Female College in Westminster, Virginia. He remained in that post until his death.
Arbogast had married Frances "Fanny" Gibbons, the sister of fellow Dickinsonian Alexander Severus Gibbons of the class of 1846, on February 2, 1858 and the couple soon had three children. Cora Lee was born in 1859, Leland Ashby in 1860, and Buford, born in 1862. Six more children followed, several of whom died in infancy. Benjamin Arbogast himself died in Winchester, Virginia on March 31, 1881. He was fifty-five years old.