There are two forces acting on the hair as a scissor closes–one to cut the hair, and one to push the hair out of the scissor. Forty-five degrees is the angle at which the cutting force becomes greater than the pushing force.
While there is more to sharpening a hair-styling scissor than getting the correct angle, you can see why your scissor will not perform at its best if it isn’t sharpened at 45 degrees (or sharper). I am not saying that at a different angle, you scissor will not cut hair, but it is not going to feel the same. In fact I can make different edges depending on the use of the scissors; Slide cutting, Point cutting, Blunt cutting in addition to razor sharp edges. The right edge design makes hair cutting easier and more precise.I was a hairstylist for many years, so I speak from experience.
When you hand me a pair of scissors to be sharpened, I inspect each part as I disassemble it at my work bench. Screws, washers, I check for nicks in the blade. I hold the blade against a “straight edge” to inspect the “set” (bend). I measure the cutting angle with my laser angle gauge. I visually follow the curves. A Japanese scissor is full of curves. The blades are bent slightly (the “set”). The cutting edge has a 800mm lengthwise curvature, and the outside of the blade curves into the cutting edge. Sometimes, the angle of the cutting edge changes as it gets closer to the tips. These curves, first have to be recognized, and then, providing they are correct, they should be followed. My Rapid Edge Machine is great, it shapes, it smooth’s, it polishes, but it all comes down to me. I see the dings and the curves; from experience, I know how to follow the curves, and finesse your scissors into cutting flawlessly.
A scissor becomes dull for a variety of reasons. You may have done a lot of hair cuts. The scissor may have fallen on the floor. There could be a nick in the blade, the scissor won’t cut properly past the nick. The screw could be misaligned, or too loose or too tight. The washer might be damaged or missing. These are just the most obvious problems, but I can think of a dozen other reasons a pair of scissors cut poorly. There are specific remedies for each problem. The trick is to know which ones to apply. For example, a slight change in the bend (set or balance) of the scissor blade can change it from bending the hair to cutting perfectly.
Since I began sharpening scissors in 1981, I have successfully dealt with all these kinds of damage. I do all the things you hope a scissor sharpener is capable of doing. I restore the cutting edge, remove nicks in the blade, fix bent scissors, corrugate edges, and align handles. I am an expert. I use a state-of-the-art, water-cooled, five-head honing machine. I have more tools than I want to count. If your scissor can be renewed, I have the equipment, and the experience, to do it right. I am mobile; I work in my van for on site appointment, or can handle mail-order scissor sharpening as well, with your scissors returned fast.