One of ten children born to Robert and Elizabeth Spear, Armstrong was born in Ireland. The Spear family immigrated to Cedar County from County Tyrone, Ireland. They were at sea for seven weeks before they arrived in New York. In 1871, Armstrong began his education at Cornell College. He graduated in 1878, not attending continuously, but teaching country school while it was in session. After college, he moved to Philadelphia, where he had family. He married Anna Armstrong, who died in 1904. He was a prominent member of the Masonic Lodge both in Philadelphia and in Mount Vernon. He married Clara Brackett Smith in 1912. He and Clara’s brother, Edgar, had been good friends during Armstrong’s time at Cornell. Clara and Armstrong lived in Brackett House, and Armstrong was a member of Cornell’s Board of Trustees. Despite being ill during the Class of 1924’s graduation, he signed 108 diplomas.