Arjuna will not fight. He is grieving for people who are still alive.
When Kṛṣṇa begins to teach, at 2.11, his first sentence is about exactly that: you grieve for those who should not be grieved for. The wise grieve neither for the dead nor for the living.
630 verses later he gives his final instruction, the verse people quote most, 18.66. It ends with two words: mā śucaḥ. Grieve not.
Everything Kṛṣṇa teaches sits between those two sentences. The Gītā is many things. It is also a long answer to a grieving man.
Going deeper
The first thing Kṛṣṇa says in the teaching is about grief. After 2.10 shows him answering the sorrowing Arjuna as if smiling, 2.11 opens his reply: you grieve for those who should not be grieved for, and yet you speak words of wisdom; the wise grieve neither for the dead nor for the living. 2.12 goes on to say that there was never a time when he, Arjuna or these kings did not exist, and there will be none when they cease to. Near the end, 18.65 asks Arjuna to fix his mind on Kṛṣṇa, and 18.66 gives the final instruction: abandon all duties, take refuge in me alone, I will release you from all sins, do not grieve. 18.67 then says to whom this should not be told. The story notes that one root for grief frames the teaching at both ends. The passages are in chapter 2 and chapter 18, and what the Gītā says about dharma follows 18.66.