Scissors have a bunch of interesting designs in them that you don't really take into account when you first begin sharpening.
Ride lines are one of those extremely important and often overlooked when it comes to sharpening and correcting a shears cutting action.
It allows some strength to the edge of the hollow grind in beauty and pet shears, and makes the cutting a much smoother, sleeker action.
Basically its allowing the blades to pass one another and make a clean cut without biting into each other causing them to loose that nice sharp edge very quickly.
There are 4 points on a standard shear and all of them should be at 90 degrees of each other with a nice consistent ride line all the way along the edge to the tip.
There are also other little tricks you can perform on texturisers like ramping the teeth.
Without having this correct the rest of the sharpening job is pretty much pointless.