There are also hilariously inappropriate times, like during sex, or to prove you are the smartest person in an argument.
Now, maybe this is just me being silly, but I'm pretty sure that you show you are smart in an argument by being correct. Sure, the issue being argued might be murky and debatable, but the facts you use to back up your side can be obviously right or wrong. For example, if you claim that China is not going to stay a dominant economic power because the Chinese economy relies on a barter system where everything is paid for in chopsticks, you are obviously wrong, because we all know things are paid for in fish balls.
If people pointed out you were literally, factually wrong about China's currency, you probably would back off and be a bit embarrassed, like a normal person, but some people somehow think they can keep up the bluff by pulling out academic credentials. "You may have an encyclopedia showing that China has actual paper currency, but I have a PhD in economics! And I graduated at the top of my class!"
These people are confused about how credentials work. In the real world, we show our GPA, test scores, and degrees to get into a school or a job, and those set up the expectation that we'll do a good job or succeed in the program. But then we actually have to do the job, or the coursework. Once you have fucked up and covered the $100 million genomics lab in burnt peanut butter or something, nobody is going to care about how many letters you have after your name. They are just going to assume you got them by fraud.
You think they would have caught this earlier.