It's because the Olympian gods, especially Zeus, thought it gave too much power to humans, and disrespected the gods - or in other words, placed humans above the gods. Gods in most ancient religions did not like being dissed at all.
Although Prometheus had supported Zeus in the war against the Titans for control of the universe, Zeus didn't like the fact that Prometheus showed so much caring for humans. In addition to giving them fire, Prometheus had taught mankind many things to help them thrive: agriculture, medicine, how to tame animals, etc. From Prometheus' point of view it was a necessary thing for mankind to survive. His silly brother Epimetheus had given all the other animals wondrous powers like flight, speed, thick furs, sharp teeth and claws, and puny humans were left with nothing - so he gave them fire, and knowledge.
Another thing he did that angered Zeus: he also tricked the gods into accepting the bad parts of an animal as sacrifice from man instead of the good parts. He showed the gods two piles of meat, one looking smooth and glossy and covered with fat, and the other looking disgusting and covered witn entrails. The gods were too short-sighted to inspect the meat piles and chose the shiny fat covered one - which was hiding a bunch of bones, while the icky looking pile was covering all the good cuts of meat. Zeus saw this is as a great insult. (Note, the sacrificial meat part isn't in Prometheus Bound specifically, but it is part of the overall mythology of Prometheus.)
Another reason why he was bound and tortured was that he was hiding a secret about a prophecy - that one day, Zeus would bear a son who would be more powerful than he, and would defeat him and take over. Given that Zeus had seized power by overthrowing his own father, this was a serious worry for him. But no matter how he was tortured, and no matter how Hermes tried to convince him, Prometheus refused to be bullied into giving up the secret.
Prometheus is generally depicted as a true friend and champion of mankind, the force of righteous anger, and resistance to the injustice of authority. The Olympian gods on the other hand (remember Prometheus was also a god since he was a Titan, but not an Olympian) were not as noble. Later on the Olympian gods became more 'good' in the literature, but at the time Prometheus Bound was written, not so much.