Kate Keller clings to superstitions, saying that
some superstitions are very nice!
For her, relying on superstition to keep alive her hope that Larry will return home is a way of grasping at straws so that she doesn't have to accept what she knows in her heart to be true: that Larry died in World War II. Therefore, she gets Frank Lubey to make horoscopes to show that the day Larry supposedly died, November 25, was a "favorable" day for him and not one on which he could have been killed. While clearly a ridiculous basis for a belief that Larry is still alive, it gives her a sense of comfort and control. Miller uses Kate's desperate clinging to superstition to show that Larry really is dead—if there were genuine hope he was alive, Kate wouldn't being going to the lengths she does to deny it.
The apple tree the family planted in commemoration of Larry's death also has a superstitious hold on Kate. She superstitiously believes the family planted it too soon and that it is a negative symbol of giving up on Larry. When it blows over in the night, she finds the news upsetting, especially as she had dreamed of Larry flying over in his plane, and she says the tree's destruction is a sign that they shouldn't have planted it.
Kate decides as well that the tree blowing over the night Ann arrives is a sign that Ann shouldn't be there. Kate doesn't want Ann and Chris to get engaged, because this means that everyone is accepting Larry's death. Kate tries to use superstitions that are self-serving to buttress ideas that she knows in her heart are false.