In the Robert fagles version of the Odyssey, Book 23 What reason does Odysseus initially believe Penelope doubts his authenticity?
In book 23, Odysseus fights and defeats the suitors. During this time Penelope is sleeping. When Eurycleia goes upstairs to tell Penelope what has happened, Penelope does not believe anything that has been stated. She stated that she needed to see things with her own eyes. Even when she sees Odysseus, she is in disbelief thinking that he is a god, who is playing a trick on her.
If you think about Penelope's situation, there is good reason for her to be in disbelief. First, it has been ten long years, since she has seen her husband. So, a certain amount of disbelief is to be expected.
Second, the gods often take human for in the epic tradition. So, this, too, was a very reasonable assumption. To believe too easily is to be gullible.
It is only when Odysseus gives a personal piece of information that only he and she would know that she believes. Odysseus gives the detail that their bed is immovable, because it was built from a tree, around which the house was also built.