People have always argued. Arguments often lead into fights. Fights can lead into battles where each party seeks to beat the other side. Battles as we think of them, are usually military campaigns. With military campaigns, you usually have someone who is planning the attack or defense. This is where weaponry comes in. In the beginning- men used their hands, then they picked up things- like stones and sticks to use in battles. Then they created machines that would throw the sticks and stones further, harder and sometimes straighter.
According to John H. Lienhard, on his web site, Engines of our Ingenuity (#458 Trebuchets), the use of trebuchets by the Chinese can be traced back to the 2nd Century AD, however, it is very possible that they were being used for years before that time.
One group of people that the Chinese probably used this new weaponry against were the Avars. The Avars were a group of nomadic Mongols. We know that the Avars were using the trebuchet by around 500AD.
We also know that one of the biggest enemies of the Avars was the Byzantine Empire. The Byzantine Empire centered around Turkey and the Balkans. We know that this group used trebuchets, too. The Byzantine Empire employed trebuchets by at least 600AD. They also had a very interesting name for the trebuchet- they called it "Helepolis" or "City Taker".
Why the trebuchet did not spread to the east as quickly is not known. However, it did finally make its way to England in 1216. Prince Louis of France attacked Dover Castle in a bid to takeover England and one piece of his weaponry was the trebuchet. We found a website, called Dover Castle and the Great Siege of 1216, by John Goodall that goes into detail about why Louis of France needed to breach the walls of Dover Castle. However, Prince Louis did not breach the walls, and with other battles and other concerns he was pulled away before finishing this battle. This left only a 9-year old Henry III to rebuild Dover Castle. That is, Henry, and whoever was helping to raise the future king. Years later, the rebuilt fortifications again withstood Louis and his seige weapons, including trebuchets.
Another story has the famous conquistador Hernando Cortez in the 1500's trying to use a trebuchet against the Mexicans. Unfortunately, the builders did not have a good understanding of the physics behind the catapult/trebuchet. The story continues with the arm rising to its full height, but then just falling back into place without slinging any projectiles. It is also said that Cortez was not impressed.