Have you ever seen one of those courtroom dramas on TV or at the movies where, in a climactic moment, a lawyer is grilling a witness or delivering an impassioned argument, and the other lawyer stands up and weakly says, 'Objection,' but the first lawyer is so overpowering and exciting that the judge doesn't even seem to care about or acknowledge the objection?
It's possible that you, too, are so dashing and your arguments are so thrilling that when you're writing an argumentative essay, you don't need to worry about what the opposing side of the argument might be... but you should probably plan for how to handle those objections just in case.
Consider why it's important to anticipate opposing views when writing an argumentative paper. Your purpose when writing this type of essay is to persuade the reader to accept your point of view on your chosen subject.
And because the success of this type of essay is so tied up with your audience - with convincing your readers that your position on the subject is the right one - you have to really pay special attention to your audience. What views and opinions do they already hold before they read your essay? Are they open and receptive to your point of view? Or are they more skeptical of your position?
You might present several brilliant and dazzling points in favor of your position, but if your reader sees things differently than you do, and you haven't made an attempt to address and make compelling arguments against some of his or her views, you're not likely to make much of an impact with your efforts at persuasion.