That vid is *amazing*, but there are better tutorials around.
With FA on, you always point in the direction of travel, and when you return the stick to centre FA will apply countering thrust to correct rolling and pitching.
This means that to turn around 180 degrees you need to fly in a semicircle, and spend most of that time looking in a direction that you don't want to go in.
Switching FA off means that your ship is free to point in any direction relative to the direction you're travelling in, and your control inputs aren't countered when returning to centre so you have to apply your own corrections.
Try this:
Fly towards a target
Switch FA OFF and immediately drop throttle to zero
Apply a little downward thrust and pitch up hard as you fly past your target
after doing a 180, switch FA back on and throttle up.
Do it right and you'll keep facing your target.
Practice on the cans in the first single player mission.
I'm no expert, but the 'handbrake turn in space' is a handy trick.