To make a convincing argument you have to fulfill all three of the following conditions:
Your terms are clear.
Your premises are true.
Your logic is valid.
If you want to critique someone’s argument, you have to show an error in just one of the following:Often it takes more than logic to persuade someone, it has to be worth it and not just true. Other times it takes less than logic, because people do things for illogical reasons because it seems beneficial. Either way, I figure it's worth at least trying to make sense.
They are using a term ambiguously.
They are using a false premise.
They are committing a logical fallacy (i.e., the argument is invalid; the conclusion does not follow from the premises).