I can either do a one pass XTG shave or two pass ATG shave. I've tried doing a one pass ATG shave and it wasn't comfortable.
It works because the beard grows at an angle from your skin. Rub your hand over your face, and you feel it smoother in places going in one direction and rougher in another. The smooth is with the grain, in the same direction the beard is growing, and the rough against the grain, moving "head on" against the beard.
The effect with shaving is that shaving with the grain slightly pushes the beard down. True, it cuts it short, but if you rub your hands against the grain, you'll still feel stubble. When you shave against the grain, the blade sort of "catches" under the beard instead of slightly pressing it down, letting you cut closer, in effect cutting it slightly under the skin. This is why those prone to beard bumps are frequently told not to shave against the grain. Shaving across the grain is sort of neutral in that it hits the beard "sideways," so to speak.
With shaving first pass with the grain, you're thinning out the stubble, but pushing it down slightly so you don't cut as close. Following across the grain catches the beard from a different direction, cutting it closer, and since it's already thinned, it makes the shave easier. Next using against the grain, you're catching the beard, cutting it off slightly under the skin, and since it's already thinned out some, there's not as much resistance.
Because there is still lather in the brush .
Logic? What's this about logic?!? Where's the logic in owning 14 antique razors, six brushes 4-5 different aftershaves, but being perfectly happy with sevral pucks of the cheapest and perhaps the most loved/hated soap in existence?