This quote suggests that platonic (non-romantic) friendships are often between two people who are either old or unattractive. It is implying that people who don’t have physical beauty or youth find comfort in forming deep, platonic friendships. This can be seen in real life, when someone who is lonely or has difficulty forming relationships finds a connection with someone else who is also lonely. This connection is closer than the more common superficial friendships, and so is categorized as a platonic friendship.