A negative connotation made to describe the choice many women have for an elective caesarean, rather than grunting and screaming for hours like they portray in the movies.
Saying "Too posh to push" is usually said by men who will never know the physical demands of pushing a child's head through their body. Similar to pushing a bowling ball through a straw.
Imagine passing an 8 pound baby out of your A-hole. Just try.