In the context of persuasive essay-writing, a counterargument is simply a statement a writer makes that opposes an initial assertion. Rather than using them simply to weaken another's argument, however, many writers take the time to brainstorm counterarguments against their own points in order to counter those. Usually, the generation of arguments and counter-arguments proceeds as follows. The writer:
- offers a thesis, such as, "Children should be encouraged to play video games";
- provides arguments in line with the thesis, with supporting evidence. Example: "Video games are beneficial for child development, as they improve hand-eye co-ordination, encourage pattern recognition and reduce child abuse rates by keeping children from annoying their parents, as the following studies in Respected Publication of Child Psychology show";
- shows counterarguments and evidence to support them, such as: "Opponents of video games say that the increasingly vast amount of time children spend playing video games has contributed to a disturbing rise in child obesity rates, as shown in the famed Well-known World Review of Obesity, and so children should be banned from playing video games"; and
- refutes the counterarguments. A writer can do this in many ways, including attempting to persuade the reader that the advantages outweigh the disadvantages or that the disadvantages are trivial.
A writer must be careful not to allow him/herself to get too carried away, however, otherwise s/he runs the very real risk of having the original point completely lost in the argument/counterargument/counter-counterargument cycle.
Some readers believe that using counterarguments in an essay gives the paper an appearance of indecision that weakens its persuasive power. This belief appears to be based on the classical rhetorical idea that a single, strong argument makes more of a persuasive impact than several equally persuasive ones. However, in the academic world, a prevailing school of thought is that it is crucial to identify objections to one's stance and pre-emptively defend against those, as by not including counterarguments, one appears either ignorant of the objections or as if one is deliberately trying to conceal valid opposing points; regardless of one's intentions, giving either of those impressions weakens one's argument.
One should note that, as a general rule, it is better to save the more complex kinds of persuasion for a written medium or a focused, sophisticated audience, as the more complex one's argument becomes, the less likely a listener will be able to retain all of it or take away a strong message from the attempt at persuasion. Thus, the single, compelling argument would be best for casual conversation, advertisement and oratory.
Be warned that if you cannot generate counterarguments for your thesis, then it is probably either so obvious that it is not worth arguing or, conversely, it is so vacuous that nobody would bother arguing against it. And it goes without saying that if you generate too many counterarguments too easily, you had better look for a new thesis. | 
