If you’d take the time to read the link supplied … Sorry about the rogue dot that got in there previously.
The boards are easy to break because the wood has been cut into lengths against, rather than with, the grain. This means grain runs across the board and not along it. No additional cutting or scoring required.
I don’t know if this wood would still be tough enough to hurt your hand. I suppose you’d have to be careful of where the knots were. But it is still very much easier to break than the lengths of wood you’d normally encounter. No timber-merchant would choose to cut wood in this way, as the resulting boards are totally useless for any kind of construction.
So, to get back to the OP, the instructor was spinning a line to stop his pupils going home and trying it out. Any wood they might have lying around at home is practically guaranteed to have been cut the correct way and be nearly impossible to chop with your hand. The fact he didn’t just own up to this, making up some nonsense instead, gives credence to Randi’s opinion that the whole ‘chopping wood’ thing is a bit of a cheap party trick.
This doesn’t mean that everything else these guys can do is a fraud or that the martial art in question has no merit. I wouldn’t want anyone deciding to come around and give me a practical demonstration!