We are taught wrong. Actually if we trace the linage of Eklavya, then we come to know that he was the nephew of Bhagwan Sri Krishna.
Once during a visit to jungle with his father he was lost. And was brought up by Nishad Raj.
When Dronacharya saw him then he realized that the boy did not have a good aura. He came to know that the most powerful Vidya will do harm to society if is taught to the Eklavya. So he did not want that the most powerful information should given to wrong motive people. This is also with Nuclear science. In these days Pakistan , North Korea has become the synonym of terror due to access of power . with good people its constructive and with bad people its destructive.Thus he asked for guru Dakshina so that he would not be a terror for the society. And the story does not end here. Eklavya was able to perform archery without his thumb. With the help of adjacent two fingers of thumb he was able to shoot the arrow.
Modern archers do this. Without thumb he became the king of Nishad and attacked on Lord Krishna’s kingdom many times due to pact(treaty) from Jarashand who was infuriated due to Vadh of Kansha.
In the final battle, Bhagwan Sri Krishna killed him.
Now you decide, a person who want to kill Bhagwan Sri Krishna then he can kill anybody with wrong motive.
Dronacharya was not an ordinary person. He was a Yogi too, there are chances that he would have known that this boy is not appropriate for this Vidya. So he asked for his thumb to neutralize his some power which he acquired due to his dedication and strong will. He did not do this so that Arjuna become the best archer in the world.
Dronacharya himself was a great archer. There was no match of Bheesm Pitamah in all over the universe, there was another legendary hero Lord Parushram.
So , whatever is taught to us to demoralize us and make our sacred scriptures unworthy. But the truth is different. We need to revive the education and teach the truth to coming generations. All the books and topics should be again researched minutely and ban the things that were misrepresented by foreigners etc. to ruin our grand culture and civilization.