June continues to reject Neil because she was about to marry someone else but was left at the altar. According to May, "June swore off men and said she would never get married" (page 152). June met Neil when he became the principal at her school, and even though she spends a great deal of time with him, she refuses to risk getting married to him. He asks June to marry him, but she continually turns him down. May, however, wants June to marry Neil because she wants her sister to be happy. May has clinical depression, and she mourns the death of her twin sister, April. May's death convinces June to get married. In the suicide note that she leaves her sisters, she writes, "It's my time to die, and it's your time to live. Don't mess it up" (page 303). This note finally convinces June to marry Neil, as May's tragedy moves her to find happiness in life.
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.