Primarily, argument has two purposes: argument is used to change people's points of view or persuade them to accept new points of view; and argument is used to persuade people to a particular action or new behavior.
Since people don't always agree on what's right or reasonable, appropriately constructed argument helps us arrive at what's fair or true. It is used to settle disputes and discover truth. Teachers assign argumentative writing so students can learn to examine their own and other's ideas in a careful, methodical way. Argument teaches us how to evaluate conflicting claims and judge evidence and methods of investigation. Argument helps us learn to clarify our thoughts and articulate them honestly and accurately and to consider the ideas of others in a respectful and critical manner.