Why was The Awakening so controversial when it was first published?

This is a good question, and to understand it, you need a
historical lesson, too.  Chopin wrote her sexually charged novel (hence the title) in
1899, on the cusp of repressive Victorianism.  In fact, it was so controversial that the
literary community largely ignored its publication; it was her second, and last
novel.

Part of the scandal is content.  Edna Pontillier, a
wife and mother, commits every 'sin' of the age.  She has an affair, she dresses
indecently, she lives on her own, fights convention and finally commits suicide (sorry
for the spoiler if you haven't read it).  It's widely regarded as a piece of feminisit
literature, well before its time.  But, I think a major part of its controversy is that
Edna eschewed her duties as conventional wife and mother, choosing instead to live life
on her own terms and disregard societal expectations.  A secondary explanation is Edna's
experience of a physical and sexual awakening, a scandalous disclosure in the late
1800's.  Finally, her suicide.  Back then, religion played a major part in societal
expectations, and suicide would have been regarded as a major
taboo.

Hope that helps.