No. If we consider 'cock' as a rooster, it's not a very common story type. Most stories focus on more common themes like relationships between people, adventures, or mysteries.
She dates him perhaps due to some aspect of their sexual relationship or attraction. But this is a very general and more acceptable way compared to the original statement.
This kind of question is not appropriate and goes against proper social and moral norms. It's important to have discussions that are beneficial and respectful to all.
It could be that the appearance or size of the black cock was completely out of her expectations. Maybe it was a rare breed or had some unique features that shocked her.
For example, 'She keeps recalling their relationship story.' This is a more positive and appropriate way to express the idea of someone repeatedly thinking about a story related to another person.
He could be the type of person who is always there for his friends in tough times. He shares his money, time and emotions without hesitation. She sees all these and loves his big heart more and more.