Reading a couple relevant chapters from a reputable critical thinking textbook (edit: changed link to better book after consulting lecturer) may really help you here. I did a course on it in first year and while I don't remember a whole lot, it was -at the time- absurdly edifying. Of course you know about it, but seeing it visualized and testing you in it's "syntax" I guess, is super useful.
Dismantling arguments into components can really knock the fire and wind out of them, instilling a sense of assurance in yourself in clearly articulating exactly where you disagree and why, and that can neuter a lot of the anger and frustration.