What is the etymology of "Tough titty"

This is a phrase I've heard used on several occasions by different people. I'm interested about what it's origins are, and whether it should be considered rude.

Essentially it means "That's tough luck!", but with an unapologetic undertone.

e.g.

Person A: Strawberry ice-cream? But I wanted chocolate.

Person B: Tough titty. That's all they had.

Chambers Slang Dictionary dates it to the 1920s, and also records the variants hard titty, tough tiddy, tough tit, tough titties and tough tits. It is defined as ‘bad luck’ and shown to produce tough tits, toots, described, accurately enough, I would imagine, as ‘a phrase of dismissal’. A hardened nipple is, presumably, less likely to deliver the sustenance, or any other comfort, normally expected of it and so those, infants or others, who encounter such an anatomical feature might be thought unfortunate.

"Tough had meant hard luck since the early 1870s, with tough luck first being recorded in 1890, tough titty in 1929, and tough shit in 1946, though this last was probably in use much earlier but wasn't recorded until changes in attitudes and morality after World War II began to allow such terms in print."

From "Listening to America" by Stuart Berg Flexner (Simon and Schuster, New York, 1982).

Source: http://www.phrases.org.uk/bulletin_board/4/messages/1024.html