Strange behaviour: Active child in inactive parent

Hello,

I have a strange behaviour in the Unity editor, a game object is inactive and its child is active. The child is considered as inactive in the scene, as I expected, but a script is attched to with a coroutine call in the start and I get an error saying the coroutine cannot be started on an inactive game object.

Is it a bug in the editor when I check the active box or is there something I misunderstand ? I know you can disable a game object in scene or in hierarchy in code, but I believed it always is a full inactive state when uncheck box in inspector.

Tanks a lot for your help.