I had a list of items to mention during extended 自己紹介 (like during a lunch or 飲み会). With those whom I also hoped to have friendship-like connection with, I'd also mention "私は次男坊です。" This allowed me to talk about my siblings which I was happy to do. And, I think it made the native speaker smile or laugh a little.
"私は次男坊です。" said alone, in a self-intro conversation, sounds funny, right? why? Would "私は長男です。" sound pretentious?
Or, I could I remembering incorrectly. I also used "次男坊ですから、許してください。" as a way to be self-depricating. In Japanese culture, the 1st born son is king, the second born is trash, so I would (to be funny) excuse my failures to being born the second son (nothing I could control). Maybe they found that 卑下 funny, and there is nothing funny about simply saying "私は次男坊です". Or maybe my overall inability to speak Japanese funny. I hope you can help me remember.