Why were the Assyrians warriors?

The Assyrians, as most other civilizations, had some people who were warriors and a vast majority who were not warriors. First, one should note that women, children, and the elderly were not warriors and that many people were farmers, craftsmen, scribes or priests, rather than being dedicated to warfare. 
Assyria was notable for being one of the first civilizations to have a year-round professional standing army. Having such an army equipped with the most recent military technology (such as iron weapons), made Assyria a powerful military force when compared with other nations in which soldiers were only trained and recruited in times of war. 
The reason for Assyria developing such a force was partially geographical. It was located in Mesopotamia, a fertile agricultural region on many active trade routes. The attractiveness of its location meant that many people were trying to conquer it. Once Assyria developed an empire, many subjected tribes tried to break away. In both cases, Assyrian kings viewed a powerful army as a solution to their problems. 
https://www.ancient.eu/Assyrian_Warfare/