In consequence of the curse of Rama (his preceptor in arms) as also of the words of a Brahmana (who cursed him on another occasion), owing also to his deprivation of the accoutrements of battle, he, in my judgment, is only half a Ratha. Having approached Falguni (in battle), he will not certainly escape with life!' Hearing this, Drona, that foremost of all wielders of weapons, said, 'It is even so as thou hast said. That is not untrue! He boasteth on the eve of every battle, but yet he is seen to retreat from every engagement. Kind (out of season) and blundering, it is for this that Karna, in my judgment, is only half a Ratha!'
Here Drona humiliates Karna more than Bhisma itself, yet Karna decided not to fight under Bhisma alone, but took up arms and fought under Drona's command.
It is for this that thy heart hath been such. Through pride, and owning also to thy companionship with the low, thy heart hateth even persons of merit! It is for this that I spoke such harsh words about thee in the Kuru camp! I know thy prowess in battle, which can with difficulty be borne on earth by foes! I know also thy regard for Brahmanas. thy courage, and thy great attachment to alms-giving! O thou that resemblest a very god, amongst men there is none like thee! For fear of intestine dissensions I always spoke harsh words about thee. In bowmanship, in aiming weapon, in lightness of hand and in strength of weapons, thou art equal to Phalguni himself, or the high-souled Krishna! O Karna, proceeding to the city of Kasi, alone with thy bow, thou hadst crushed the kings in battle for procuring a bride for the Kuru king! The mighty and invincible king Jarasandha also, ever boastful of his prowess in battle, could not become thy match in fight!
Here Bhisma reveals why he hurt Karna during the tales of Ratha and Atiratha and says his reason for claiming him to be Half a ratha (during his death bed). Yet Drona with no clue of what's going in the mind of Bhisma, just blatantly agreed to him or is this a hint of Drona too was aware of Karna's birth secret ?
So is this a custom way back then, of focusing on the one who started the conversation than the one who joins in the middle ? I don't see how he ignored Drona's comment, but was deeply concerned about Bhisma's comment alone.