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In my humble opinion, it's a good idea in a persuasive essay to at least acknowledge counter-arguments. If you simply ignore counter-arguments, and a reader is aware of them, his response is likely...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/9272 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
In my humble opinion, it's a good idea in a persuasive essay to at least acknowledge counter-arguments. If you simply ignore counter-arguments, and a reader is aware of them, his response is likely to be, "Well, he just completely ignored the fact that X." As Paul Clayton says, if you give the pro, then the con, then with no rebuttal or reply to the con you give your conclusion, it can make the argument look weak or disconnected. It can come across as, "Here is my argument, here is why my argument is flawed, but I'm just going to ignore the flaws and stick to my original thesis." When I am writing a persuasive essay, I don't end with counter-examples. I may end with counter-examples followed by rebuttals. More often, I start with the position I disagree with, then show why it's wrong, then give my conclusion. But there are many ways to structure an essay. The shorter an essay the less time you're going to spend on rebuttals. In a 5-paragraph essay I might well skip rebuttals as there's just no time to get into them.