Ha! Of course I agree, but, anyway, I don’t ever say impossible. Every time I think I’m sure about something (chicken and otherwise) I am amazed to learn something new.
There is such a thing as gyandromorphs, half and half birds, which are both sexes.
Here’s the article
https://www.npr.org/templates/story/story.php?storyId=124529630
There is a current thread about this very subject —-that their isolated rooster appears to have laid an egg, and they do have photos:
https://www.backyardchickens.com/threads/strange-did-my-rooster-lay-this-egg.1444906/
And a previous thread from 3 years ago, also w photos...