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It depends on what the "point" of the essay is, and how it's set up in the intro/thesis. If the goal of the essay is to argue "dogs make great pets," then there shouldn't be a counter-argument at ...
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#4: Attribution notice removed
Source: https://writers.stackexchange.com/a/9270 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/9270 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
It depends on what the "point" of the essay is, and how it's set up in the intro/thesis. If the goal of the essay is to argue "dogs make great pets," then there shouldn't be a counter-argument at all. If the goal is to present both sides of a point, then the intro needs to say that, and I would suggest Para 2 is the Pro, Para 3 is the Con, and maybe Para 4 discusses which is stronger or has more weight. At the moment your two-pro/one-con feels lopsided. In any case, I would certainly put pro arguments before con arguments, so you're heading in the right direction.