I have not flown for many years. Does security examine woman's breasts and if so why?

Normally they do as a part of security measures...

At the O'Hare, everyone has to go through security scan machines, if in question one or two TSA agent will manually scan the person with a handheld metal detector, if there is still in question, the TSA agent may request to body search you at a more private location... If you don't want to be hand searched don't wear anything that can potentially cause suspension that had to be strip searched. TSA agents at the ORD have guidelines and generally friendly.

I've never seen security specifically examine breasts, and whenever my scan wasn't "all clear", I was never even touched. They just wave a wand around you. So, as far as I know, the answer is: No.

Security Examines everybody's everything, to maintain secure travel.