Lord krishna asked Arjuna to fight because he had to carry out his duty as a kshatriya and not because dharma was at stake, which was secondary. This is the most basic understanding of Bhagvad gita. If one cannot understand this, he should reach a ISKCON center and render service.
Secondly, as Harshad pointed, there are only 2 varnas in the beginning of the kali; vaishnavas and shudras and after the goldern era; shudras alone. Hence there is no question of kshitriyas and no question of killing, which if carried out will only be sin and sin and nothing else.
Sankirtan is the only yuga dharma.
Kali yuga will be worse, it is already predicted and repeats every maha yuga again and again. It is such a basic and simple thing that it is preplanned and its a lila of Krishna. Hence Krishna is telling just mind your
business of remembering me as per rules and regulations of that particular age.
Thank you
Hare krishna