The maesters were an order of intellectuals in Game of Thrones, and a certain theory suggests that they killed the world's surviving dragons to rid Westeros of magic. Here's an explanation of the Grand Maester Conspiracy, including how the men could have carried out the dragon killings.
The Order of Maesters was comprised of scholars, healers, and advisors. Those who served the order swore to a sacred oath while leaving behind their family and political allegiances. The headquarters of the order was located at the Citadel in Oldtown. After men trained and studied vigorously, they obtained the "maester" title before they were assigned to a castle belonging to a noble family. Almost every castle within the continent had a maester on hand to provide educational support and counsel, especially for the children. Many maesters have become highly skilled in ravenry which they use to send long communications throughout Westeros.
Maesters vowed to serve Westeros by providing their intellect but according to the Grand Maester Conspiracy, the group may have had a hand in a larger mission. The conspiracy theory believed that the maesters helped destroy the dragons well before the events of Game of Thrones. Centuries before the series began, House Targaryen reigned supreme in Westeros. That was until their civil war known as the Dance of Dragons. Following the war, King Aegon III chained up the remaining dragons in Dragonpit and presumably killed them. That said, a line from Maester Marwyn in A Feast for Crows hinted that the maesters actually did the killing in order to assist in eradicating magic. The statement from Marwyn the Mage came while speaking to Samwell Tarly:
“Who do you think killed all the dragons the last time around? Gallant dragonslayers armed with swords? The world the Citadel is building has no place in it for sorcery or prophecy or glass candles, much less for dragons.”
Why The Maesters Wanted To Kill The Dragons In Westeros
It was a known fact that maesters hated magic and thought the world would be better off without it. The main reason for ridding the world of magic was because they wanted a reliance on scientific knowledge. Magic was unpredictable and not fully understood so that would hurt the maesters' sole purpose of existing. With magic so prevalent, especially with the existence of dragons, maesters would lose control as their expertise and knowledge would be questioned. Maesters also believed that much of the conflict over the past few centuries was due to magic. They felt that dragons only led to destruction and more unrest among humans.
How The Maesters Destroyed The Dragons
The Citadel was the home to a massive library that the maesters had access to, so it's very possible that the order poisoned the remaining dragons, not King Aegon III as previously suggested. This would fall in line with what Maester Marwyn stated in George R.R. Martin's A Song of Ice and Fire novel. With a lifestyle that prioritized learning, they could have easily studied how to poison a dragon. It was also a coincidence that dragons, as well as other forms of magic, seemed to disappear for a long time after the death of the species. They even used the years that followed to try to keep all information that involved magic under lock and key. This could be why maester-in-training Sam had to sneak into the forbidden section at the Citadel to research White Walkers during Game of Thrones season 7.