brahma-bandhur na hantavya
kuru pratisrutam satyam
yat tat santvayata priyam
priyam ca bhimasenasya
pañcalya mahyam eva ca
Translation by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
The Personality of Godhead, Sri Krsna said: A friend of a brahmana is not to be killed, but if he is an aggressor he must be killed. All these rulings are in the scriptures, and you should act accordingly. You have to fulfill your promise to your wife, and you must also act to the satisfaction of Bhimasena and Me.
Purport by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
Arjuna was perplexed because Asvatthama was to be killed as well as spared according to different scriptures cited by different persons. As a brahma-bandhu, or a worthless son of a brahmana, Asvatthama was not to be killed, but he was at the same time an aggressor also. And according to the rulings of Manu, an aggressor, even though he be a brahmana (and what to speak of an unworthy son of a brahmana), is to be killed. Dronacarya was certainly a brahmana in the true sense of the term, but because he stood in the battlefield he was killed. But although Asvatthama was an aggressor, he stood without any fighting weapons. The ruling is that an aggressor, when he is without weapon or chariot, cannot be killed. All these were certainly perplexities. Besides that, Arjuna had to keep the promise he had made before Draupadi just to pacify her. And he also had to satisfy both Bhima and Krsna, who advised killing him. This dilemma was present before Arjuna, and the solution was awarded by Krsna.