Actually, since I am a student of traditional Taekwondo, I have more of a connection with karate than I do with modern Taekwondo. Given the path that modern Taekwondo has taken (commercialized sport), if I had it to do over again, I would have probably stayed in karate. There are no traditional Taekwondo schools in my city/county, so I train at a school that comes the closest.
I haven’t researched the physics behind selected breaking, but I am sure there is a scientific explanation. Like all other supposed mystical things in the martial arts, I am sure this one is also just a stunt. As you have noticed, long and/or thin is always easier to break than short and/or thick. Ever see the demo where assistants break 2x4 boards over various parts of the “masters” body. The boards a always long and impact at the center of the board’s length. You do not see them trying the same thing with a baseball bat length board.
Selective breaking demos always use brittle, manmade objects One reason is probably because pliable, natural objects, such as wood, have numerous unpredictable factors that affect their breakability, whereas, manmade materials are consistent throughout and thus their breakability is predictable. It is also possible that objects are specially selected for certain characteristics, are placed in a particular way, or are pretreated in some way.