Glasser was born on May 11, 1925, in Cleveland, Ohio, to Ben Glasser, a watch and clock repairman, and his wife Betty. He attended Case Western Reserve University in Cleveland, where in 1945 he earned his BS in chemical engineering. After a short career as an engineer, Glasser returned in 1946 to Case Western, but instead, during his first semester, was drafted into the US Army and stationed at Dugway Proving Ground in Utah. He returned to Case Western in 1947, earning his MA in clinical psychology in 1949 and his MD in psychiatry in 1953. He completed his medical internship and psychiatric residency at UCLA and the Veterans Administration Hospital, respectively, and became board certified in 1961.