https://www.youtube.com/watch?v=JikA1Edw2F0
The writer of the song explains his intentions here.
Host: 선생님, 이 곡을 만드신 데는 무슨 동기가 있을 것 같은데요. You must have some motivation for making this song, Mr Kim.
Kim: 예, 이 노랫말을 읽- 그 처음에 보면은, 키 크면 싱겁다는 말이 있습니다. 이 가사를 체가 처음 본 순간에, 제 옆 반 선생님이 참 키가 크고 싱거워요. 그래서 그 선생님을 생각하면서 우리 생활 주변에 이 재밌는 얘기를 좀 싱겁고 재밌게 표현해봤습니다. Yes, there is a saying that goes "if it's tall, it is dull". When I have first come up with this lyric, the teacher in the class next to mine is really tall and dull. So, this teacher in mind, I tried to express this interesting everyday phrase in a bit dull but also fun manner.
Host: 노- gets interrupted
Kim: 그냥 싱거운 이야기 나온 김에, 저희 반 담임하는 아이들이, "선생님!" 하고 걱정을 해요. "왜 그라는데?" 물어봤다며는, "서울에 가시면 이번 곡을 심사하실 분이 키가 크신 분들이 나오면 어떡해요!" 하고 걱정을 합디다. Speaking of dull stories, my homeroom students were worried, saying "Mr Kim!". When I asked "What's the matter?", they told me "When you go to Seoul, what if the judges who rate the song have tall people in them?"
Host: 네, 키 크고 싱거운 분 계십니까? 네, 뭐 아무도 일어나시지 않는데요, 키 커도 싱겁지 않으신 모양입니다. 걱정하실 것 없고요. Ah, (looking at the judges and the crowd), is there a tall person who's also dull? (pauses) No one seems to stand up, that must mean even if they're tall, they are not dull. There's no need to worry.
As for the old saying, I believe the original proverb is "키 크고 싱겁지 않은 사람 없다", which the dictionary explains, "키 큰 사람의 행동은 야무지지 못하고 싱겁다는 말" It means that a tall person's actions are clumsy and dull.
I don't know where the proverb comes from, but I personally can think of two hypotheses:
When people look at tall people, they have higher expectations for them in certain things. When it turns out they aren't much better, people are disappointed.
"Tall people" originally referred to grownups, and children are in general much more colorful and full of liveliness than grownups.