Surely there must be exceptions to this rule.

Although it is thankfully very rare, there are times where you feel compelled to mention your degree, such as when you're in an argument with someone who read a Wikipedia article on something covered by your field of study, and they're acting like that makes them an expert. It's even worse if you've actually spent your entire career working in that field.

Hypothetical example: You have a degree in biology and have spent 10 years working as a field biologist, say for evaluating environmental impact studies or some such thing. Then some guy at a party is blathering on about how stupid all the environmental protection laws are, and how he read some articles about it. He's spouting off a mix of half truths, lies, and just plain ignorant statements in rapid fire succession, and keeps mentioning how much he's read about it. Somehow you get pulled into the conversation, and start to politely refute his nonsense. He just doubles down on it and keeps reminding you of all the articles he's read and all the "research" he's done (i.e., Google University). Do you mention the fact that you have a biology degree and 10 years of experience dealing with the very thing he's ranting about?