Reasoning doesn't work well with young children because they really don't have the ability to think logically yet. This ability develops around age 8.
I suggested that instead she try comforting him by labeling his feelings: "You're sad because it's not your birthday and so you're not the one getting the gifts. You really would like a present too wouldn't you?" Although he won't be getting a present, Mom's compassion and understanding will help him deal with his emotions and feel better.