Abbey was born in Seattle, Washington in 1932 to Sam and Brenta Abbey. His father was born in London but had emigrated to Canada, returning to Europe to serve in the First World War. After being injured in France, Sam returned to London to recuperate where he met Bridget, later changing her name to Brenta, who had moved to the capital from the village of Laugharne in Wales. Sam and Bridget married and their first child, a boy, was born in Wales before the couple moved to Canada before settling in Seattle. Abbey attended Lincoln High School there. He received his bachelor's degree in general science from the United States Naval Academy in (Annapolis, Maryland) in 1954; and a master's degree in electrical engineering from the U.S. Air Force Institute of Technology at Wright-Patterson Air Force Base, Ohio, in 1959.