Why is carrot cake a bad idea in this situation?
She says that carrot cake is a "bad idea" here because she is worried that Kate is offended and doesn't like her cake. The cake is a cake made only of carrots, and there is no actual cake inside. She made this cake for her because it is healthy and Kate is on a diet and is trying to avoid eating things like cake. But Kate wasn't actually offended by the cake, she is just upset about something else.