Question

why is it important to consider your audiences opinions when making an argument

Answer 1

Because you want to catch your audiences attention, and when you have an argument you want to win, going against what the audiences opinion is then they wont like you or your argument because you spoke against their opinions. 

Answer 2

Taking into account the other party's opinion while making an argument allows you to form a response that is directly related to what that person's stance on a subject is. This is very helpful, because this allows arguments to remain civil, and you don't have to assume as much about the argument taking place.