Yeah, that’s one of my pet hates, too. I knew a guy who used to do that, and was very explicit about the fact that he felt it gave him some sort of upper hand (literally and figuratively) in the encounter. Complete idiocy.
I also dislike the limp dishrag handshake. A nice firm grip—whether you’re shaking with a man or a woman—is what i like.
Ah an old secret I remember from way back. People in non-electric wheelchairs have extremely strong hands and arms. Had a friend in junior school who was wheelchair bound, he was ruler of any arm wrestling match.
I find the use of the second hand good when you want to be warm and sincere, or when it will change into a hug, but also with someone you don’t trust at all. The reason for the final one is it gives an air of sincerity that your lack of trust may otherwise show through, and two it makes it very possible to throw or break the arm of that person. So should a bully try to get you to shake hands in a threatening situation it works quite well.
I try to give a medium-firm handshake. I usually get either the bone-crusher (hurts even more when you have arthritis, tendonitis, and several rings on your fingers) or the limp dishrag (just plain insulting) from men. Women who do shake my hand seem to usually get it right.