Pre-PC days, a gentleman never imposes on a woman, it is her prerogative to acknowledge him. A handshake between the sexes is initiated by a woman, if they are good friends, she is the one who offers her cheek for the buss, he does not plant one on her of his own volition. The same rules apply for age, the older of the two, men or women, is the one who initiates the handshake, the one to whom the courtesy is directed.
I don't know how they're teaching it these days.
Hmm. Well, then, good for him for not having imposed on her and good for her for having barely acknowledged him.