When you pull a friend's stuck car with your car using a chain, there's a right way and a wrong way to do it. Bear with me, this will make sense in a minute. If you are the one doing the pulling, you want to sloooowly pull forward until the chain is taut (snug, tight), and only then give it more power to try to pull the other vehicle. This is important! People who don't know any better will back up so the chain is slack, then GUN their engine, thinking a lot of power and speed are needed to yank the stuck vehicle loose. WRONG! What this will do is snap the chain.
Now what does this have to do with the broomstick method of dispatching a chicken? This. If you grab the chicken's feet and yank up hard and fast, there's a good chance you will decapitate the chicken, blood will squirt everywhere, the chicken will flap like crazy, splashing blood all over you and you will be so traumatized you'll never do it again. So don't do that!
Instead, gently hold the chicken head down for a moment to relax it. I know, I know - this is not the way you want to carry your chicken around on a general basis. But its life is going to be over in a few minutes anyway, and this is a form of anesthesia. Now scrape a little groove on the ground where its neck is going to be. May as well make it comfy. Lay your "broomstick" over the bird's neck just behind the head. Place your feet on the broomstick, one on each side of the bird's head. Grasping the bird's feet, gently but steadily pull up until the neck is stretched taut. Do it fairly quickly. Then give one more quick yank upward, without first dropping your hands. You may feel a "pop." The bird may thrash, but the deed is done. I like to have a bucket handy with a trash bag in it to drop the bird into immediately. Close the bag and tie it shut. This is especially handy if you did pull too hard and there is bleeding. And that's it!