The second chapter answers Arjuna twice, and the two answers rest on incompatible foundations. The first is metaphysical. The self is not born and does not die; it is not cut, burnt, wetted or dried; it discards worn bodies as a person changes worn clothes. If that is so, grief for the men opposite is a category error, since what Arjuna thinks he would be destroying is not destructible and what is destructible was going to end anyway. The second is social. Arjuna is a warrior, this is a just fight that has come to him unsought, and to withdraw would earn a dishonour worse to a man of his standing than death.
Neither argument satisfies Arjuna and neither is meant to be the book's conclusion. The first proves too much, since it would equally excuse any killing. The second is an appeal to reputation, which the rest of the Gita will spend seventeen chapters undercutting. Read as a sequence they look like a teacher trying the available moves before making the one that matters.
That move arrives in the second half, and it changes the subject. Krishna introduces action performed with the mind fixed on the doing rather than on what the doing will yield. A person has a claim on the work and no claim at all on its fruit, and should not therefore make the fruit the motive, nor should they take refuge in not acting. This is the hinge of the whole book. It does not tell Arjuna what to do. It tells him what to want while doing it, and by doing so it dissolves the collision of duties that paralysed him in chapter one.