My Dad and Granddad too. Funny, most of the wimpy handshakes come from guys. Do guys change their handshakes when they shake a girl's hand?
Generations------I taught my sons to wait to offer his hand for a hand shake from a female. The female may not want to touch him, if she offers then fine.
Along these lines I find some men especially in business get surprised when a woman holds our her hand, it is like they expect this behavior from a male, but seldom a woman.
Hubby does not trust the Glad Hand men that will shake hands with the devil. Those that he has just met that slap him on the shoulder or what not ,he cringes from.
Me, if I have not seen someone in awhile and they male or female come over and give me a hug then I know they are a true friend and I don't smell bad.