The problem you're making is that you're trying to talk to someone who is upset through logic, when that's not how human psychology works. It's also why trying to rationale with someone who is upset in the middle of a game is usually not very effective.

The way human emotions work is that they come from the primitive lizard part of our brain, and then we process those emotions through the more advanced parts that developed later (the frontal cortex) which is also where things like logic are accessed from.

The thing is that when someone is upset or experiencing any kind of negative emotion, their ego automatically activates and it blocks the access to our frontal cortex.

This means that they're unable to not only process those emotions in that moment but also unable to think logically or with rationale, because their brain has blocked access to that part.

So when you're saying things like "Just think about this for a minute" and the guy doesn't care, it's because they physically can't function with logic in that moment which is why it's a waste of time trying to have a discussion.

At the same time as the persons stress level goes up, their cortisol goes up and it encourages black and white thinking and they're unable to see nuance.

So ultimately these kinds of "therapy" strategies in League are not very effective for winning at all. People might have the idea that it helps because they like to believe that they have the ability to calm people down but in general it doesn't tend to work too often in the middle of a game when someone is genuinely upset.