In "The Necklace", why do visits to her rich friend always fill the young woman with despair?
According to de Maupassant in the story "The Necklace", Madame Loisel
...had a friend, a former schoolmate at the convent, who was rich, and whom she did not like to go to see any more because she felt so sad when she came home.
This friend is arguably the woman who is now known, as an adult, as Madame Forrestier, who is still rich and quite fortunate. As the story says, Mathilde would feel "sad" when she came home each time she would go see her friend. This is because Mathilde had dreams of also being rich. The problem with Mathilde is that she believes that she deserves all those good things. That is not a problem in itself, but considering her situation and her reality she is literally outside the realm of reason.
She felt that she was born to be privileged and that she was entitled to receive things, and be famous. She may even have a narcissistic streak that makes her truly believe that all of that is true. However, Mathilde's dreams go beyond merely wanting a better life station for herself. She was quite extravagant in her thoughts.
She thought of long reception halls hung with ancient silk, of the dainty cabinets containing priceless curiosities and of the little coquettish perfumed reception rooms [...] with men famous and sought after...
This shows that, even if she had been as rich as Madame Forrestier and had she been born rich, she would have still not been satisfied. She would have wanted more. Mathilde's false sense of reality makes her exaggerate things and make more of everything than what there is to the eye. Therefore, while she may be "sad" to have a richer friend, it is likely that Mathilde would have been said regardless of her status in life because of her constant state of dissatisfaction.