mccook was born in columbiana county, ohio. his family was prominent in army service — his father daniel mccook and seven of alexander's brothers, plus five of his first cousins, fought in the war. they were known as "the fighting mccooks", for whom mccook field in dayton, ohio, was named. his brothers daniel mccook, jr., edwin stanton mccook, and robert latimer mccook were all union generals, as were his cousins anson g. mccook and edward m. mccook.