Jerry is an orphan, and so it's inevitable that he keenly feels the lack of a mother. That being the case, it's understandable that he should lie about having one. He's using his rich, vivid imagination to fill the mother-shaped hole that lies at the heart of his life.

It's a well-known psychological phenomenon that children will often invent imaginary friends as a way of dealing with their fears and anxieties of the outside world, and that's pretty much what Jerry's doing here. Most children find life hard to deal with at some point, but for a young orphan like Jerry, it's even harder. Pretending that he has a mother— someone who watches over him, loves him, and cares for him—makes life just a little bit easier to deal with.

The reason that Jerry lies about having a mother is not directly stated in Marjorie Rawlings's short story "A Mother in Mannville." Readers must make inferences as to the reason. Here are some things to think about to help in making inferences: 

1. Jerry is twelve years old and living in an orphanage. He develops a friendship of sorts with the narrator, who is renting a cabin near the orphanage in order to do some writing. Jerry falls in love with the narrator's dog and spends time with him while the narrator is away. 

2. Jerry is often invited into the cabin as it gets colder. The narrator describes the chats she has with him, as well as the times he and her pointer dog Pat doze in front of the fire together while she writes. This must have felt like the closest thing to a family he'd ever known. 

3. When people have challenging circumstances in their lives, they often escape into imaginary realities in order to cope with their present difficulties.