No breastfeeding on airplanes!

In the news: Woman kicked off plane for breast-feeding - Travel News - MSNBC.com.  A similar situation happened in my backyard last year.  A mother from my gym was breastfeeding her baby at the lake and got a ticket for indecent exposure!  When I was nursing my baby I ran into a few people that were uncomfortable with it in public - mostly people I knew - but I never was asked to leave or stop.
Why do people have such a problem with women breast-feeding in public?  Is a woman's breast that offensive or is the sight of a baby eating offensive?  Or is it the fact that a baby sucking on a breast brings up sexual imagery in their minds and that makes them uncomfortable?  I think it's the latter and that happens because our society has made breasts (and the bigger the better) into pure sex symbols.  We've forgotten what they  are really there for - feeding babies!
Can they be both?  Sex symbols and for feeding babies?  Or does the one taint the other?