Aslan promises that the tree which Digory planted will protect Narnia from the Witch for many years as a "Shield." Why will she "loathe" the tree and want to avoid it? 

Because she ate one to meet her heart’s desire, like the sentence” all get what they want, they do not always like it”. and it was also the warning on the golden gates” take of my fruit for others or forbear, for those who steal or those who climb my wall shall find their heart’s desire and find despair”

The Witch stole and ate the fruit for herself and climbed the wall in the wrong way, so she fulfilled her desire and then she would find that the length of days with and evil heart is only length of misery, that would despair of herself.

When she came down into Narnia with a hundred miles of the tree, she would find death and horror and despair from the tree’s smell. She would loathe it and wanted to avoid it.