Disloyalty is the name for that breaking of support: the act, or the habit, of not standing by your friends, your country, or your group. The person is disloyal; what they did is disloyalty. Selling a secret, changing sides, running down people who trusted you — those can all be called disloyalty. Though actually, like the adjective, it is a judging word, and the line is not always agreed. In history class it often means political betrayal. At home it might mean repeating something private. It is formal. When the hurt is sharp, everyday English often prefers betrayal. When it is milder, people just say that wasn't loyal. Watch the grammar: disloyalty is a thing, not a person. You show disloyalty; you are not a disloyalty.