The Catechism of the Catholic Church reads:

The forms taken by modesty vary from one culture to another. Everywhere, however, modesty exists as an intuition of the spiritual dignity proper to man. It is born with the awakening consciousness of being a subject. Teaching modesty to children and adolescents means awakening in them respect for the human person." (C.C.C. # 2524)

People here are not serious, they repeat slogans and polemics very superficially. The nipple taboo is found across pre-Christian and non-Abrahamic societies, probably because of breasts' association with fertility. I.e

When did bare breasts become taboo in Western civilization?

Probably around 3,000 years ago. Women are displayed with exposed breasts in Minoan artwork from 1500 B.C. Some historians believe that these ancient women went topless only during religious rituals—bare-breasted, buxom goddesses have been worshipped since the dawn of civilization—but some of the artworks depict everyday activities, suggesting that bare breasts may have been commonplace. Just across the Mediterranean, ancient Egyptian women sported elaborate dresses that could either cover the breasts or leave them exposed, depending on the whim of the designer. Over the next few centuries, however, breasts become strictly private parts. Ancient Athenian women were wearing flowing, multilayered robes that concealed the shape of the bosom by the middle of the first millennium B.C. Spartan attire was more risqué, exposing the female thigh, but breasts were always covered.