Albert Barnes Commentary Matthew 5:36

"Neither shalt thou swear by thy head, for thou canst not make one hair white or black." — Matthew 5:36 (ASV)

Thy head. This was a common oath. Many of the Gentiles also used this oath. To swear by the head was the same as to swear by the life, or to say, "I will forfeit my life if what I say is not true." God is the Author of the life, and to swear by that, therefore, is the same as to swear by Him.

One hair, etc. You have no control or right over your own life. You cannot even change one single hair. God has all that control; and it is therefore improper and profane to pledge what is God's gift and God's property; and it is the same as swearing by God Himself.