Breasts are one of the most obvious traits of sexual dimorphism in humans and as they are sexually selected for. Sexy boobs equals sexy grand children. The notion that we are 'educated by society' as males to find breasts attractive is totally absurd - the attraction is genetic. Equally absurd is the notion they are not a 'sexual organ'.
Random trivia time - enlarged breasts are found during periods of lactating in primates, which is also a signal that females are unable to reproduce. It's hypothesised that enlarged breasts were selected for by our ancestors as it encouraged monogamy by hiding the tell tale signal of when females were unable to reproduce - hence 'tricking' males into thinking they were always ready to reproduce and providing for them, benefiting those females with larger breasts, leading towards the sexual dimorphism we see today.
Bingo: breasts are a sexual indicator, as well as for feeding young. The human equivalent of a baboon's big red arse. If they were only for nursing, they would be much smaller - just like our great ape cousins'.
I dont think that should necessitate them being covered up, however.