As I don't know the story, I can't determine its moral. But generally, stories about animals can have morals like the importance of hard work, friendship, or being brave.
I'm not sure specifically which 'little brother bigger cock story' you are referring to as the name is rather unclear and could potentially be something very specific or even made - up. Without more context, it's difficult to say what it's about.
One possible story could be about a little cock in a petting zoo. Some unruly children keep chasing it and trying to pull its feathers, which is a form of torment. The little cock tries to hide among the other animals at first. Eventually, it finds a kind zookeeper who scolds the children and protects the little cock. After that, the little cock becomes more confident and less afraid of the visitors.
Definitely not. When we think of well - known stories, we think of classic fairy tales, famous novels, or well - documented historical accounts. This title doesn't match any of those common types of stories, so it's highly unlikely to be well - known.
I'm not really sure there are specific 'little cock tip torment stories' in common fables. Fables usually focus on moral lessons through the actions of animals like the fox and the crow, not this rather strange concept.
Another possibility is that it's a misnomer or a play on words. Maybe there was a misunderstanding at some point that led to this phrase being used in your family stories. It could be that a small item was thought to look like a part of a rooster in a very humorous and innocent way, and that's how the 'little cock' stories started.