I chicken wing. I cup & saucer. And I have been doing those things for a long time. For those but lately arrived in the shooting sports, those terms refer to small details in the way you hold a rifle and a pistol. They used to be right and proper things to do, but now they are supposedly passé. To hear some Internet commandos tell it, doing these things is gravely in error and a sure sign one is dull. Holding your guns in these ways is now out of fashion, if you please, and those of the high speed, low drag contingent on teh interwebz want you to know it.
Who asked them? If you are doing something that works for you, I suggest you keep on doing it. There are several advantages to these techniques. Thrusting your right elbow straight out when shooting a rifle, or even angling your elbow up a little from horizontal, creates a pocket in the shoulder joint to hold the rifle's butt securely in place. It also helps in controlling recoil. The recoil control aspect does not matter if you are shooting a .223, but not everyone shoots those.
The cup & saucer grip is a technique developed for the double action revolver. It does a fine job of keeping the thumb and fingers of your support hand out of the way of the long, double action trigger stroke and the moving hammer. People who have not learned how to do it claim that the firing hand will jump out of the support hand when you shoot, but that is easily avoided, with most calibers, by exerting a bit of downward pressure with the firing hand onto the support hand's palm--isometrics, you know.
|How to chicken wing a rifle|
|How to cup & saucer a pistol|
People love to feel superior and tell other people what they are doing wrong, a human trait as reliable as it is deplorable. What I would like to point out, for the benefit of interweb commandos, is that these old and supposedly passé techniques work as well as they ever did, which is rather well, thank you very much.