It's not always who you are arguing against.
In any argument your goal will determine your audience. While it is possible that you may have more than one audience, typically one will be primary. When I am in Court my goal is to persuade a Judge to rule in my favor. He or She is my audience. Secondarily my client is also an audience because, even if I lose, it will be important that I my client sees that I have made the best possible argument in his or her favor.
Rarely is your audience the person against which you argue. How few minds have been changed in Facebook debates! That's true if you consider only the minds of the antagonist and protagonist. However the onlookers, the bystanders who read your arguments may be persuaded.
Once you know your audience you know how to tailor your argument, what words to use, what tone to adopt, and what "buttons" to push. In some ways it can be like the famed game Apples to Apples, or it's more naughty and races counterpart - Cards Against Humanity. You pick a card that may not make sense to you, or even to the group, but rather you pick the card that you think the person having to choose is most likely to relate.