ŚB 1.7.53-54

Arjuna was perplexed because Aśvatthāmā 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 brāhmaṇa, Aśvatthāmā 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 brāhmaṇa (and what to speak of an unworthy son of a brāhmaṇa), is to be killed. Droṇācārya was certainly a brāhmaṇa in the true sense of the term, but because he stood in the battlefield he was killed. But although Aśvatthāmā 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 Draupadī just to pacify her. And he also had to satisfy both Bhīma and Kṛṣṇa, who advised killing him. This dilemma was present before Arjuna, and the solution was awarded by Kṛṣṇa.