I’ve now sussed how to do it. It’s really graceful, a lovely way of doing things. The trick behind it is that two folds get performed in just one movement. At the same time, when you demonstrate to someone (or watch the video the first time) it doesn’t quite seem to make sense.
The stumbling block is that whilst you fold the tshirt over its own front, the resulting fold leaves the shirt-face up and puts the bend in the back of the t-shirt.
The first time I did it right, I jumped. You just don’t expect action a to lead to shape b. The fold at the beginning is fine; it’s the pull-through that’s weird, because so much of the topology seems to change in that single pull. It feels like you’re doing something inside-out, except you’re not at all, and it’s the pull-through that makes it all work out. I’m reminded in some ways of an un-knot; it feels like doing a knot but just doesn’t work like one.
That’s why I think it seems so strange and incomprehensible, to begin with, anyhow. It also is neat, elegant, a great way of doing things, and a fun thing to show friends. And hey, it makes me smile every time I do it.