Have you ever been talking to someone and noticed they dropped the fact that they were in a relationship into the conversation, even though it didn't seem relevant? To hear someone do it it can be annoying if you think their opinion of themselves is so high that they need to warn you that they aren't available, because of course you should be attracted to them. Well, here's one reason they might do it that could make you feel a bit better about yourself and more empathetic towards them:
They could be attracted to you and feel uncomfortable with their attraction towards you. Their unnecessary mention of their monogamous relationship might be a warning to people they're attracted to: "Don't tempt me, I can't control myself." This would ultimately be a sign of insecurity in their ability to be monogamous.