In just three short lines, the speaker waves away one subject and quietly steps toward another. "Don't ask me about insanity" sounds almost breezy, like someone declining a topic at a dinner party. Insanity is the big, dramatic word, the one people expect when they think of mental struggle. The speaker doesn't claim any special knowledge of it.
Then comes the turn: "depression, on the other hand..." The dash and the trailing ellipsis do a lot of work. The sentence never finishes, and that silence suggests there's plenty to say, though the speaker can't or won't say it. Judging by the phrasing, depression is something they know firsthand, or at least far better than insanity.
The mood is dry, wry, and a little heavy. There's a hint of dark humor in the casual tone, but the unfinished ending leaves a quiet ache. What goes unsaid carries the weight.