Grandfather Bheesma saw in Drona Acharya sufficient knowledge of the Bow and Arrow. He knew Drona could be very instrumental in the education of the young Kurus. Bheesma was fully cognizant that knowledge of the Bow and Arrow was an essential skill needed by all the young warriors.
Drona having had many hardships in his youth was motivated by revenge and power. During the years when the Kurus were young he was a confidant of the elders and became materially very comfortable. King Dhritarashtra was blind and old age was surely creeping up on him. His agility of mind and clear thinking was diminishing. Vidura and Bheesma were not at all a threat to Drona because he was needed and held in high esteem. His skills spoke loudly for themselves and so he manipulated the affairs of the Kingdom as he desired.
When the young warriors grew up and Yudhisthira was anointed crown prince, Drona continued to advise the young man and at times would get very disturbed because Yuthisthira would always make decisions on the side of Dharma. He realized he could not manipulate Yudhisthira as had been done with King Dhritarashtra and decided the time had come to insert a wedge between the party of Yudhisthira and the Son of the blind King. The instrument that carried the wedge was Drona's own son (Aswattamma). Drona watered the root of the creeper (jealousy) within the heart of Duryodhana. Many rumors began to circulate within the Kingdom and the wedge separated the two parties even further.
Drona wanted Duryodhana to be crown prince because he knew he was weak and could be easily influenced. With Duryodhana in power he could then satisfy his long time quest for fame and position -MahaBharata