What is the purpose of a counterargument in a persuasive text?

A counter argument is necessary, in order to show one's audience that one has taken into account the opposing opinion/thesis of the argument but still sides with their opinion/thesis; it allows the writer to once again prove their thesis. 

Both brothers died in the battle.

Explanation: The reason for the battle being... "Both Eteocles and Polyneices were supposed to rule Thebes jointly. One was to rule one year and the other would rule the next year. However Eteocles refused to give up power to Polyneices once his year was over. So, Polyneices fled to Argos, raised an army, and attacked Thebes. Both brothers were killed in the battle,"

So this would be the Climax/ Rising Action