Based upon evidence in the text, the authors of the Bhagavad-Gita were concerned with family.
It easily can be said that most people care deeply for their family members, and wouldn't do anything to harm them intentionally. Like-wise, when Arjuna sees his intimate kinsmen on the opposing side of battle, he nearly loses his will to fight. He becomes so upset he says "My limbs sink, my mouth is parched, my body trembles, the hair bristles on my flesh"(27). If the thought of killing in war wasn't bad enough, having to oppose his family is just too much. Arjuna plainly states "I see no good in killing my kinsmen in battle" (27). Arjuna would more readily give up everything good that could come of battle (like land, kingship, and other riches) if it meant he would have to kill family members.
This shows that the authors really cared about family-bonds and honoring kinsmen. The authors wanted to show that nothing should come between a family, not even a war. They considered it a terrible thing to act wrongfully against ones family. This is even seen today when one observes the close ties between family members. Even if you aren't thrilled with your family members, the saying goes that "blood is thicker than water". Thusly, as Arjuna puts it, the authors would "lament the great sin we commit when our greed for kingship and pleasures drives us to kill our kinsmen" (29).