Why does June continue to reject Neil and why is May against her rejection?

In the book The Secret Life of Bees,
June is a very headstrong and educated woman.  She and her sisters have had to make a
way in the world for themselves.  They have learned the benefit of being independent. 
June also feels responsible for her sister May.  By resisting the desire to marry she is
ensuring that she stays with her sister, August, in taking care of
May.

However, the biggest issue keeping her from marriage
is that June had to overcome was her own fear of rejection.  On page 211 of the book
there is a paragraph that tells how June was supposd to be married, but the man had
backed out of it.  Since then she had been afraid of love and would not take another
chance.

May knew that Neil was a good man and she also knew
her sister's heartfelt feelings.