In a closed facebook group on analytic philosophy, someone asked a question along these lines: "How do you primarily criticize other people's reasoning?"
Here's the reply I gave. What are some other ways you approach the task of evaluating another's reasoning?
There's no definitive checklist or prescription for identifying an issue and diagnosing someone's treatment of that issue. One reason such an endeavor cannot be reduced to an algorithm is that the complexity of any single issue can be daunting, and the product of interactions among such issues is of an order of complexity too high for even the best merely human mind to address synchronously or sequentially.
Instead, we have to use various troubleshooting heuristics until we've isolated a matter of interest that fits our capacity for analysis. At that juncture, we can go to town on it, and perhaps make (micro-)progress toward clearing away the underbrush of human cognition and laying out defensible assertions about how and why things are.
Typical questions in the area of fuzzy diagnostics applied to person P include (but are not limited to):
- What is the general domain that P is addressing, and what general domain does P seem to believe P is addressing? Do these match?
- What are the purposes of P's discourse? To identify an assertion and rebut it? To identify a confusion and clarify it? To rant gracefully against a disfavored ideology? To note an oversimplification and introduce remedial complexity? Other?
- What does P assume? Does P acknowledge that P assumes that?
- When fluff and qualifications and mods and idiosyncratic terminology and other debris have been swept away, what is P's argument? What conclusion does P claim to reach? Which premises does P offer as an avenue to reach it? What evidence does P adduce in support of them?
- What kinds of evidence are actually relevant to P's argument? What kinds of evidence does P employ? What kinds does P ignore? What kinds does P dismiss? What is the effect of this particular configuration of employment, ignorance, and dismissal on P's endeavor?
- Which alternatives to P's affirmations and inferences does P explicitly consider? What does P prefer to them? Which explicit judgments account for P's preference? Which unacknowledged factors constrain it?
- Does P's argument, taken as facially acceptable, pass the "So what" test?
- If you find fault with P's argument in its given context for reasons such as those suggested above, is there something about your own approach, your own assumptions, your own preferences, or your own commitments that prompt or guide you to object in that way?
- Is P right?
- What would you have to know or reliably believe in order to evaluate P's discourse in each way listed above? Are you suitably positioned to evaluate it?
Note: this is not an exhaustive list– not even close. It's also given not in a chronological or diagnostically relevant order; it's given in the order in which I improvised the list while eating a bagel and superficially weighing your question.
The broad point is that there's no formula for doing philosophy. Instead, there's a set of habits of mind intermixed with some balance of generosity, skepticism, curiosity, and hope.