Final answer:
The Loisels don't tell Mathilde's friend the truth about their debt because they are ashamed and want to maintain the perception of a happy and comfortable life.
Step-by-step explanation:
The reason why the Loisels don't tell Mathilde's friend the truth in the story is because they are ashamed of the fact that they have gone into a lot of debt in order to replace a necklace that Mathilde had lost. They don't want their friend and others to know about their financial troubles because it would not only be embarrassing, but it would also shatter the perception that they have a happy and comfortable life. They believe that maintaining a facade of wealth and happiness is more important than being honest about their financial situation.