It is discovered that Yugiri has never laid eyes upon Murasaki, the woman who acts as his mother. Why does Genji wish to keep her hidden?

Genji fixes things to prevent Yugiri from every seeing Murasaki, especially now that he is becoming a young man. He remembers how he fell in love with his own stepmother, Fujitsubo, and he does not want that to happen with Yugiri and Murasaki. Genji fears that Yugiri will fall in love with Murasaki.