If the son of a ksatriya declines to fight, he is a ksatriya in name only, and if the son of a brahmana acts impiously, he is a brahmana in name only. BG 1972 purports

Expressions researched:
"If the son of a ksatriya declines to fight, he is a ksatriya in name only, and if the son of a brahmana acts impiously, he is a brahmana in name only"

BG Chapters 1 - 6

If the son of a kṣatriya declines to fight, he is a kṣatriya in name only, and if the son of a brāhmaṇa acts impiously, he is a brāhmaṇa in name only.

BG 2.3, Translation and Purport:

O son of Pṛthā, do not yield to this degrading impotence. It does not become you. Give up such petty weakness of heart and arise, O chastiser of the enemy.

Arjuna was addressed as the son of Pṛthā, who happened to be the sister of Kṛṣṇa's father Vasudeva. Therefore Arjuna had a blood relationship with Kṛṣṇa. If the son of a kṣatriya declines to fight, he is a kṣatriya in name only, and if the son of a brāhmaṇa acts impiously, he is a brāhmaṇa in name only. Such kṣatriyas and brāhmaṇas are unworthy sons of their fathers; therefore, Kṛṣṇa did not want Arjuna to become an unworthy son of a kṣatriya. Arjuna was the most intimate friend of Kṛṣṇa, and Kṛṣṇa was directly guiding him on the chariot; but in spite of all these credits, if Arjuna abandoned the battle he would be committing an infamous act. Therefore Kṛṣṇa said that such an attitude in Arjuna did not fit his personality. Arjuna might argue that he would give up the battle on the grounds of his magnanimous attitude for the most respectable Bhīṣma and his relatives, but Kṛṣṇa considered that sort of magnanimity mere weakness of heart. Such false magnanimity was not approved by any authority. Therefore, such magnanimity or so-called nonviolence should be given up by persons like Arjuna under the direct guidance of Kṛṣṇa.