I entirely agree with your first two thoughts. I believe the compulsion effect was perhaps a bit lazy on my end. It has since been removed.
Additionally, the concept of "the perfect argument", to me, means an assertion that has layers on layers of evidence to support it, an argument so strong that no one can oppose it. This extends even to the personal level, for topics such as, "I should/should not divorce my partner" or "I should/should not commit suicide". The perfect argument effectively convinces people to follow it; if the answer to the previous examples is yes, then that person would be fully persuaded into doing it.
Perhaps this is reaching a turnaround point where it's not the person holding the SCP, but rather those who listen to the arguments from that person, which would add another layer of complexity I'm personally not ready for.
Finally, your last thoughts about how the SCP makes people think they have a perfect understanding goes against what I originally intended. It is an interesting thought but, respectively, I would prefer it my way. For me, SCPs are horror, or at least darker in nature. While, granted, it would be comedic if the person under the SCP's effect merely thought that they were correct, it is not what I had in mind. For me personally, it is much scarier to be granted the immense amount of knowledge that could potentially come with the ability to create an infallible argument.
EDIT: I have given it more consideration, and will attempt to work the idea concerning the illusion of intelligence into the work.
I had an idea to extend the SCP's effects to make them permanent, making those under its effects forever unable to hold regular conversation, as everything would boil down to a debate. However, maybe this isn't great as too many people with this affliction would get annoying and difficult.
Lastly, I will explain my reasoning for posting here on the Ideas and Brainstorming forum over the Drafts and Critiques forum. Essentially, every post I make follows the same format as this one; that is, a tab under a Sandbox page that has a semi-completed work inside. Frankly, I'm not great at just banging out a paragraph with my thoughts - I have to get really into character/detail before posting what I consider to be a good idea.
In the past, I posted drafts just like this one on the Drafts and Critiques board, where I would frequently be chastised for posting there. They would tell me to get my ideas reviewed here in Ideas and Brainstorming, so I figured I would come here. I'm not sure where to post my ideas because they seem to be a mixture of both an idea and a draft.
EDIT: To you, or anyone else's knowledge, is there an SCP that already exhibits these properties? That is always one of my main concerns when writing one; I would love to know if there was a way to quickly scan through existing SCPs to make sure the core concept isn't already taken.
In any case, thanks again for taking the time out to respond and critique my work.