Using Counterarguments in your papers
The following information is from your Hacker’s
Rules for Writers book:
Do not ignore sources that seem contrary to your position of that offer arguments different from your own. Instead, use them to give voice to opposing points of view and to state potential objections to your argument before you counter them (Hacker 463).
Anticipate objections; counter opposing arguments
Readers who already agree with you need no convincing, but indifferent or skeptical readers may resist your arguments. To be willing to give up positions that seem reasonable to them, readers need to see that another position is even more reasonable. In addition to presenting your own case, therefore, you should consider the opposing arguments and attempt to counter them
(Hacker 93.)
Anticipating and countering opposing arguments
To anticipate a possible objection to your argument, consider the following questions:

Could a reasonable person draw a different conclusion from your facts or examples?

Might a reader question any of your assumptions?

Could a reader offer alternative explanations of this issue?

Is there any evidence that might weaken your position?
The following questions may help you respond to a reader’s potential objection:

Can you concede the point to the opposition but challenge the point’s importance or usefulness (meaning that you accept or acknowledge they may be correct, but continue to explain why their point may not be important or useful)?

Can you explain why readers should consider a new perspective or question a piece of evidence?

Should you respond to how your position responds to contradictory evidence?

Can you suggest a different interpretation of the evidence?
When you write, use phrasing to signal to readers that you’re about to present an objection. Often the signal phrase can go in the lead sentence of the paragraph:
 Critics of this view argue that…
 Some readers might point out that…
 Researchers challenge these claims by…
It might seem at first that drawing attention to an opposing point of view or contradictory evidence would weaken your argument. But by anticipating and countering objections, you show yourself as a reasonable and well-informed writer. You also establish your purpose, demonstrate the significance of the issue you are debating, and ultimately strengthen your argument.
There is no best place in an essay to deal with opposing views. Often it is useful to summarize the opposing position early in your essay. After stating your thesis but before developing your own arguments, you might have a paragraph that addresses the most important counterargument.

Or you can anticipate objections paragraph by paragraph as you develop your case. Wherever you decide to address opposing arguments, you will enhance your credibility if you explain the arguments of others accurately and fairly (Hacker 93).
Here is some more good advice from The Writing Center, University of North Carolina at
Chapel Hill:
Counterargument
One way to strengthen your argument and show that you have a deep understanding of the issue you are discussing is to anticipate and address counterarguments or objections. By considering what someone who disagrees with your position might have to say about your argument, you show that you have thought things through, and you dispose of some of the reasons your audience might have for not accepting your argument.
You can generate counterarguments by asking yourself how someone who disagrees with you might respond to each of the points you’ve made or your position as a whole. If you can’t immediately imagine another position, here are some strategies to try:
 Do some research. It may seem to you that no one could possibly disagree with the position you are arguing, but someone probably has. For example, some people argue that the American Civil War never ended. If you are making an argument concerning, for example, the outcomes of the Civil War, you might wish to see what some of these people have to say.
 Talk with a friend or with your teacher. Another person may be able to imagine
 counterarguments that haven’t occurred to you.
Consider your conclusion or claim and the premises of your argument and imagine someone who denies each of them. For example, if you argued “Cats make the best pets.
This is because they are clean and independent,” you might imagine someone saying
“Cats do not make the best pets. They are dirty and needy.”
Once you have thought up some counterarguments, consider how you will respond to them—will you concede that your opponent has a point but explain why your audience should nonetheless accept your argument? Will you reject the counterargument and explain why it is mistaken?
Either way, you will want to leave your reader with a sense that your argument is stronger than opposing arguments.
When you are summarizing opposing arguments, be charitable. Present each argument fairly and objectively, rather than trying to make it look foolish. You want to show that you have seriously considered the many sides of the issue and that you are not simply attacking or caricaturing your opponents.
It is usually better to consider one or two serious counterarguments in some depth, rather than to give a long but superficial list of many different counterarguments and replies.
Be sure that your reply is consistent with your original argument. If considering a counterargument changes your position, you will need to go back and revise your original argument accordingly.
Source: http://writingcenter.unc.edu/handouts/argument/

Here is part of another resource (check it out, it’s very comprehensive and complete) from
Shoreline Community College:
Organization
Where does the counter-argument go?
The short answer is a counter-argument can go anywhere except the conclusion. This is because there has to be a rebuttal paragraph after the counter-argument, so if the counter-argument is in the conclusion, something has been left out.
In practice (there are exceptions), the rebuttal is usually not the concluding paragraph, which means that generally the counter-argument is anywhere but the last two paragraphs.
Counter-arguments can be very effective in introductions, especially if you are arguing against a popularly held view. However, it’s also very common to place them after the presentation of the case for the thesis. In other words, they would go after all of the main points that support the thesis, but before the conclusion—in the third-to-last paragraph, with the rebuttal in the secondto-last. This is probably the most common position.
Generally, unless there is some compelling reason specific to the particular argument being made, it does not make sense to put the counter-argument in the middle of the case for the thesis.
In other words, you would not typically present two points in support of the thesis, then the counter-argument and rebuttal, and then more points in support of the thesis.
Here are two outlines showing the most common placement of the counter-argument. The first is probably the most common.
I.
Introduction
II.
Supporting point #1
III.
Supporting point #2
IV.
Supporting point #3
V.
Supporting point #4
[there can be any number of supporting points]
VI.
Counter-argument
VII.
Rebuttal
VIII.
Conclusion
I.
Counter-argument, which also serves as introduction
II.
Rebuttal, which would usually include the thesis statement
III.
Supporting point #1
IV.
Supporting point #2
V.
Supporting point #3
VI.
Supporting point #4
[there can be any number of supporting points]
VII.
Conclusion
How should the rebuttal be introduced?

If the counter-argument requires careful signaling, so does the rebuttal. The essay has just done a
180° turn away from its thesis, and now it is about to do another 180° turn to complete the circle.
The reader needs warnings and guidance or they will fall off or get whiplash—you’ll lose them, in other words, because the essay will seem incoherent or contradictory.
The common strategies for introducing the rebuttal are the mirror image of those for introducing the counter-argument, and they all boil down to the same basic concept: “Yes, but....” They can be as simple as that, or as complex as this example sentence:
While Auerbach’s claim seems initially plausible, and is backed by the copious evidence provided by his astonishing erudition, it is marred by an inconsistency that derives from an
unsupportable and ultimately incoherent definition.
In all cases, the job of this transitional language is to show the reader that the opposing view is now being answered. The essay has returned to arguing its own thesis, strengthened by having taken the opposition into account. Here are some typical strategies. These are generic examples; they work best when tailored to suit the specifics of the individual topic.
 What this argument [overlooks/fails to consider/does not take into account] is ...
 This view [seems/looks/sounds/etc.] [convincing/plausible/persuasive/etc.] at first, but ...
 While this position is popular, it is [not supported by the facts/not logical/impractical/etc.]
 Although the core of this claim is valid, it suffers from a flaw in its
[reasoning/application/etc.]
Source: http://www.shoreline.edu/doldham/101/html/what%20is%20a%20c-a.htm#why
Now look back out your own claims from the previous activity. Take some time to brainstorm possible counterarguments below. Then, exchange your ideas with a partner.
Did you find similar possible counterarguments? Can you help each other decide where readers may have objections to your/their claims? Be prepared to share with the class.