Chullin 79 - Does "It and its offspring" Apply to Males?
The prohibition to slaughter an animal and its offspring on the same day applies to female animals and their offspring, but not to male parents - these are the words of the Sages, but Chananyah says that it applies equally to both.
The Sages compare the situation to that of a mother bird hovering over her young in the nest, where the mother bird is mentioned specifically and must be sent away. Chananyah says that you can't compare the two: sending away the mother bird does not apply to a nest that you own, whereas "it and its offspring" applies even to stray animals that are not yours.
Actually, the Sages agree to Chananyah in this, however, they say that "it" means only one parent, and now by analogy with the bird it must be the mother! And Chananyah, what does he have to say now? He answers that "it" means the father, and "its offspring" implies the mother.
Practically, if the father is known with certainty, then it should not be slaughtered on the same day as its offspring, even though one does not violate a definite Torah prohibition.
Art: Martin Johnson Heade - Two Hummingbirds At A Nest