CrossRoads:
as soon as you write it low, you immediately (mere microseconds later) write it high.
Well, but it's a loop. 
So, after setting pin i LOW, milliseconds later, pin i+1 goes HIGH. By the way; I've gotten the same results with a while loop:
i = 2;
while (i<10)
{
digitalWrite(i,HIGH);
delay(1000);
digitalWrite(i, LOW);
}
raschemmel:
Which pins of the level shifter chip are you referring to in this statement ?
Pins 21 to 14 (B1 to B8). On the other side, pins 3 to 10 (A1 to A8) are connected to the LEDs. The control lines are both grounded, wich means "B data to A bus" which seems correct to me in this case.