It seems difficult for me to gulp it down that inspite of enmity and getting defeated to drona how did he send his son to learn warfare . Drupada was a king himself and he should have his own warfare experts.
The reasons were following:
- New found friendship between guru Drona and king Drupada;
- Guru Drona acquiring half of the kingdom of king Drupada; had to return the favour by educating his son in weapons
From Adi Parva, it's well known story that king Drupada had insulted Guru Drona when the latter asked for a portion of the wealth. He retaliated back with the help from PAndava-s to capture the king as part of Guru dakshina.
After a time when the Pandavas became skilled in arms and sure aims, demanding of them his fee, he again told them these words, 'Drupada, the son of Prishata, is the king of Chhatravati. Take away from him his kingdom, and give it unto me.' Then the Pandavas, defeating Drupada in battle and taking him prisoner along with his ministers, offered him unto Drona,
Later they resolved their differences and became friends again.
The king of the Panchalas, thus addressed by the wise son of Bharadwaja, told ... these words, 'O high-souled son of Bharadwaja, blest be thou, let it be so, let there be eternal friendship between us as thou desirest!' Thus addressing each other and establishing a permanent bond between themselves, Drona and the king of Panchala, ... went away to the places they came from.
Somewhere inside, the king Drupada was still felt humiliated of his defeat.
But the thought of that humiliation did not leave the king's mind for a single moment. Sad at heart, the king began to waste away.
Most likely Drona was aware of the long term happenings, but he served his Dharma considering it to be a destiny.
And the great Drona, bringing the Panchala prince into his own abode, taught him all weapons in requital of half the kingdom he had formerly taken from Drupada. The high-souled son of Bharadwaja, regarding destiny to be inevitable, did what would perpetuate his own great deeds. [source]
Possibly Drupada may not have considered Drona as his enemy. But Mahabharata became an opportunity to settle the score.