Born in Istanbul, Ottoman Empire in October 1914, Kuneralp was the second son of Ali Kemal, a journalist, writer, and politician, by his second wife, Sabiha Hanım. Ali Kemal was a political opponent of the nationalists at the time of the British, French, and Italian Occupation of Constantinople, during the Turkish War of Independence. He was detained when the revolutionaries won in 1922 and taken to Ankara to an Independence Tribunal, but the ferry (or train) he was put on stopped at Izmit and there he was murdered by young Turkish soldiers. After the kidnap and murder of his father his mother took the family into exile in Switzerland. There he received his education, and a Law doctorate from the University of Bern in 1938, where he also joined the fraternity "Zähringia Bernensis".