Question

Where does the counterclaim go in an argumentative essay?

Answer 1

A counterargument should appear shortly before the conclusion of an argument essay.

In order to show that you've done well rounded research, you should always add a counterargument and refute that in your essay. This means you bring up an opposing point, and then give more detail on how your position overcomes that opposition. It should appear after you've given the reader the bulk of your research (but before your conclusion). 

Answer 2

In an argumentative essay, the order should go:

Intro

Claim

Counterclaim

Evidence for claim/against counterclaim

Conclusion

The counterclaim should be placed after your claim. That way, the opposing argument is presented, but it is not the main focus of your essay. Details as to why your claim is correct should be placed after the counterclaim, so that you can strengthen your argument before concluding your essay.