It's good to be passionate about your studies.
It's not good to suffer to the extent that you are.
The objective view of the academic problem you described is that getting better at analyzing logical arguments is good training for you in your studies, regardless of which argument turns out to be valid in the long run. However, it sounds like you have a hard time detaching your self-esteem from the question of which one is valid.
There is a way to desensitize, and develop more detachment. It's called Exposure and Response Prevention, and it was discovered as a treatment for Obsessive-Compulsive Disorder. (Important note: I am NOT expressing an opinion as to whether you do or do not have OCD.)
Here is an interesting quote from an article about OCD by Fred Penzel:
In the 19th century, OCD was known as the "doubting disease." OCD can make a sufferer doubt even the most basic things about themselves, others, or the world they live in. I have seen patients doubt their sexuality, their sanity, their perceptions, whether or not they are responsible for the safety of total strangers, the likelihood that that they will become murderers, etc. I have even seen patients have doubts about whether they were actually alive or not. Doubt is one of OCD's more maddening qualities. It can override even the keenest intelligence. It is a doubt that cannot be quenched. It is doubt raised to the highest power. It is what causes sufferers to check things hundreds of times, or to ask endless questions of themselves or others. Even when an answer is found, it may only stick for several minutes, only to slip away as if it was never there. Only when sufferers recognize the futility of trying to resolve this doubt, can they begin to make progress.
I'm not sure your particular trigger of discomfort could be found in any of the books on self treatment for OCD. I used Amazon Look Inside to check one such book with very positive reader reviews and it seemed to me that it would be quite annoying for you to try to work with. However, the description of the technique and what happens physiologically might be useful for you. It's in Chapter 4 of The OCD Workbook: Your Guide to Breaking Free, by Bruce Hyman and Cherry Pedrick.
I have written about my family's experience with ERP in this answer. (But note, that question is quite different from yours.)
Here is your description of what triggers your strong reaction:
When I hear people talking loudly about things I (like to pretend I) know something about and their opinions sound just wrong to me and it would be inappropriate to go over there and have a discussion. Or listening to authorities on the radio when I disagree with them. I seem to hate disagreeing with people without having a chance to tell them so.
If you want to work on this with ERP, on your own, Step One would be to make a list of situations that make you itch to show someone the error in his reasoning. It would be good to try to come up with at least ten different situations. You could write a draft and then come back to it a few times to see if you can add some situations to the list.
The next step, after you have a good-sized list, is to rank them according to how hard it is to keep quiet about the person's erroneous reasoning (or "reasoning" if you will).
It is often possible to do the ranking in one sitting. However, it's probably a good idea to put the ranking away for a few days before proceeding on to the next step. The list, with the ranking, is called a "map" or "hierarchy."
To explain the next step, let me suppose that the situation that ranked as a "1," in other words, that caused the least discomfort, is the following:
I am in at the fish counter in the grocery store, waiting my turn, and the fish counter clerk is telling a customer absolute nonsense about how to cook the fish the customer is buying.
Let's say this is something that has happened to you at least once, and is reasonably likely to happen again, because a particular clerk at your local store likes to shoot off at the mouth, without really knowing anything about cooking fish. (This is just an example.... Bear with me.)
Now you could structure an exercise around this. It could be, for example, hang out at the fish counter for a while at a high-traffic shopping time. Listen to the clerk spouting nonsense. Write down at intervals how strong your itch is to make a correction. You could use a 1 to 7 scale or some other scale. You can find out what a good interval is for you through trial and error. My son was told to check his "temperature" at one minute, two minutes, five minutes, ten minutes, twenty minutes, etc. But we found the following to work better for him: 10 seconds, 20 seconds, 30 seconds, 40 seconds, one minute, one and a half, two, two and a half, etc. (Those are approximate.)
You have to hold yourself back from making the correction. As time goes by, you will see the urge to correct subside. It often increases before it decreases, and sometimes the curve has two humps. But it does subside eventually.
It is possible to do this alone or with a friend or relative in a "coach" role. The coach shouldn't reassure you, but it is okay for the coach to help you find something funny about the situation.
You have to repeat the exercise approximately every day. It usually takes my son about 10 days to get to where the exercise is no longer challenging.
When you're done with Item 1 from your list, you proceed on to Item 2.
You may find it helpful to take notes about your physiological response as you are resisting the urge to provide a correction.
What's going on: your body cannot sustain the high adrenaline response indefinitely. After some time (it might be five minutes, it might be two hours), your body will stop fighting, you won't feel that strong urge to explain just how wrong the clerk is, and you'll be able to go home.
The key to the whole approach is that you progress through the situations in a very graduated, step by step way.
It can be helpful to use calming breathing techniques as one is doing the exercises.
Alternatively, you could work with a therapist. The International OCD Foundation helped me find someone in my area. (There is a shortage of therapists trained in doing ERP.)