"Relationship" based on a lie with a person not hiding the truth about herself or having a relationship while hiding the truth about yourself.
Shige knows rumours about Igarashi cutting herself, but how will he deal with knowing it's actually the truth.
Dunno why Kaname and Igarashi don't openly express their feelings, there's nothing shameful really and that will move up Igarashi confidence as she wouldn't be seen as an outcast.