Aśvatthāmā was condemned by the Lord Himself, and he was treated by Arjuna just like a culprit, not like the son of a brāhmaṇa or teacher. But when he was brought before Śrīmatī Draupadī, she, although begrieved for the murder of her sons, and although the murderer was present before her, could not withdraw the due respect generally offered to a brāhmaṇa or to the son of a brāhmaṇa. This is due to her mild nature as a woman. Women as a class are no better than boys, and therefore they have no discriminatory power like that of a man. Aśvatthāmā proved himself to be an unworthy son of Droṇācārya or of a brāhmaṇa, and for this reason he was condemned by the greatest authority, Lord Śrī Kṛṣṇa, and yet a mild woman could not withdraw her natural courtesy for a brāhmaṇa.
Even to date, in a Hindu family a woman shows proper respect to the brāhmaṇa caste, however fallen and heinous a brahma-bandhu may be. But the men have begun to protest against brahma-bandhus who are born in families of good brāhmaṇas but by action are less than śūdras.
The specific words used in this śloka are vāma-svabhāvā, "mild and gentle by nature." A good man or woman accepts anything very easily, but a man of average intelligence does not do so. But, anyway, we should not give up our reason and discriminatory power just to be gentle. One must have good discriminatory power to judge a thing on its merit. We should not follow the mild nature of a woman and thereby accept that which is not genuine. Aśvatthāmā may be respected by a good-natured woman, but that does not mean that he is as good as a genuine brāhmaṇa.