As a Brahmin, his Varna-dharma was not fighting. And since Krishna was right there, why didn't he counsel Drona not to fight?
श्रेयान्स्वधर्मो विगुण: परधर्मात्स्वनुष्ठितात् | स्वधर्मे निधनं श्रेय: परधर्मो भयावह: || 35||
śhreyān swa-dharmo viguṇaḥ para-dharmāt sv-anuṣhṭhitāt swa-dharme nidhanaṁ śhreyaḥ para-dharmo bhayāvahaḥ
BG 3.35: It is far better to perform one’s natural prescribed duty, though tinged with faults, than to perform another’s prescribed duty, though perfectly. In fact, it is preferable to die in the discharge of one’s duty, than to follow the path of another, which is fraught with danger.