First, be aware of the inappropriateness of such topics. When in a conversation, if someone brings it up, firmly change the topic. For example, start talking about a new movie or a book you've read.
The phrase 'comparing cocks stories' is rather ambiguous. It could be a play on words. Maybe it's related to comparing tall tales or exaggerated stories in a rather strange or humorous way. Without more context, it's difficult to determine its exact meaning.
It really depends on the nature of the story. In a more fictional or children - friendly 'comparing cocks story', there could be other talking animals as characters. They could be friends or foes of the cocks. For instance, a wise old owl might be a character who gives advice to the cocks about the futility of excessive comparison. Or a mischievous fox could be trying to take advantage of the cocks' preoccupation with comparing themselves.
I'm not sure specifically which 'comparing cocks story' you are referring to. It could be a story about comparing roosters in a farmyard context, perhaps about their size, strength, or behavior.
Stories about friends comparing their knowledge in different fields are also great. For instance, in history, who knows more about a specific era, or in science, who has a deeper understanding of a particular theory. This kind of comparison promotes learning and friendly debates.
No. Comparing in such a vulgar way is inappropriate and not acceptable in civilized society. It violates the norms of good taste and respect for others.