I'm honestly very opinionated about how logic courses should be taught, mostly stemming from one opinion: Don't teach fallacies before you teach how to construct a good argument.
When you teach someone fallacies first, they learn how bad arguments look before they even have a chance to make good ones, which isn't how most other subjects are taught. We teach people good writing before we teach them things to avoid.
More importantly, by giving such a focus to fallacies, you convince people that the way to critique an argument is to figure out the name of the fallacy that's being committed, drop that name in their face, then smugly wait for them to change their position.
But, if you take arguments on like this, you'll never actually analyze the flaws of the argument and you'll certainly not explain *why* that fallacy is a problem.
This is problematic in a number of ways. First, there's some bad arguments which are bad for reasons other than any of the fallacies on the list you memorize, and you can't critique those accurately because you'll always call upon one you know or none at all.
Second, if you take a sound or cogent argument and you add premises to it which are false or create fallacious argumentation, it's still a sound or cogent argument, so long as the premises which made it sound or cogent before are still there.
This means that an argument can have a fallacy in it and still work, so you can point to a fallacy in their reasoning, be entirely correct that it's there and that it's bad, and still not disprove their argument.
Finally, fallacies are just not very good ways of thinking about bad arguments. For example, here's a professional philosopher talking about just that. https://maartenboudry.blogspot.com/2017/06/the-fallacy-fork-why-its-time-to-get.html
Specifically the problem is that fallacies all either apply to such a specific case such that they're almost never used, for example post hoc ergo propter hoc, that is things happening in sequence don't imply causation, is fallacious as:
P1: A happened after B.
C: B caused A.
But, generally, people don't argue like that. Instead, they're more likely to make the much more inductive argument:
P1: A happened after B.
P2: No other thing C seems to be the cause of A.
P3: B could be the cause of A.
C: Therefore, B probably caused A.
But that isn't a fallacious argument. It is finding a causal relationship from two events happening in succession, but it's not concluding it has to be the cause, just that it's probable.
So that leaves us with two options for most fallacies. Either they're so strict that they almost never apply or they're so broad that they're not at all fallacies.
So, if not fallacies first, how should logic be taught? Well, that's simple. You teach logical form and you teach how to make arguments well, then you teach how to apply making good arguments to critiquing bad arguments.
And, when you do critique bad arguments, you do it by finding how they differ from good arguments, not how they fit into general forms of bad arguments.
This requires you to analyze bad arguments to understand what makes them bad more than just comparing them to various fallacies which forces you to explain what about them makes them bad.
So, anyway, that's my thoughts on how logic should be taught.