"Turn to him the other cheek also" is often read only as a command about physical violence. The social world behind the saying adds another dimension: blows could function as deliberate acts of insult and humiliation in an honor-conscious society.
Jesus places the example among teachings about retaliation. The issue is not that injury is unreal, but that the disciple's response is not to be governed by the ordinary demand to answer insult with insult or injury with injury.
In the ancient Mediterranean world, public honor and shame carried substantial social weight. A slap or blow could therefore be experienced not merely as pain but as an assault upon standing and dignity. The precise mechanics sometimes proposed for which hand struck which cheek go beyond what Matthew explicitly states, but the insulting and humiliating dimension of such a blow is important context.
Jesus' wording follows his reference to "an eye for an eye and a tooth for a tooth." He moves from regulated retaliation to a deliberately nonretaliatory response.
The cultural background prevents the saying from becoming a vague maxim about being agreeable. Jesus describes a situation in which a person has been wronged and publicly dishonored.
Knowing that setting makes the teaching more demanding: the disciple is not to let the normal cycle of insult, honor-defense, and retaliation dictate the response. The passage does not make humiliation good; it challenges retaliation as the means by which one's honor must be restored.