The anti-retaliation teachings assume social ranks: Roman/Israelite, rich/poor, powerful/weak. At this point, however, Jesus focuses on horizontal relationships—with neighbors and equals. Gospel understandings gave guidance for personal relationships, not only with those in the social hierarchy, but also with those in the same circumstances.
This admonition parallels the beatitude on mercy (v. 7). Someone who asks for food is, at least temporarily, in an inferior position. The person being asked might take advantage of his superiority to conserve his goods, but Jesus instructs those who may sometimes require assistance to be generous when they can assist others.
Book of Mormon Context: This particular saying confirms the Nephite egalitarian gospel first spelled out by King Benjamin: “And also, ye yourselves will succor those that stand in need of your succor; ye will administer of your substance unto him that standeth in need; and ye will not suffer that the beggar putteth up his petition to you in vain, and turn him out to perish” (Mosiah 4:16 and accompanying commentary).
Nephite society struggled for centuries, its prophets calling it to return to egalitarianism and to resist incipient hierarchies. Benjamin’s admonition makes the same point as the Savior: generosity toward others.