Exactly as mattsz says: it's all about giving yourself three full strokes to build up the crankshaft speed, so it goes through the penultimate (intake) and final (compression) strokes as fast as possible.
If you start your kick at the bottom of the compression stroke (which is where I think you are referring) then any fuel that was drawn in during the intake stroke several seconds previously will have dropped out and it most likely won't fire at the top of the compression stroke anyway.
So, it's not that you can't kickstart it from any point in the cycle, simply that it is much easier and more reliable to do it the way singh5 shows.