If I remember right you have to click on the dad during when he is near the tree during the evening. After defeating the rooster I may wrong because I've been only playing the updates and haven't started a new game for a long while.
Viewing post in Rewind: A Looping History comments
The Dad? No, that's how you get extra training events leading up to the day of the rooster's death. To feed the 'rooster' to your family, you need Chicken Immunity Title, then do all the chicken catching events (Marla Training Event in afternoon/evening, can't remember which) which will only end in the consumption of the rooster if Chicken Immunity is among your titles.