Let's start by taking a look at all the places hunting pops up in the myth of Cephalus and Procris:
Cephalus is a hunter, and he's actually hunting when Eos kidnaps him. Kind of ironic, right? Though Cephalus is out on the prowl for some prey, he's the one that gets preyed upon. Oops.
After Cephalus flips out on Procris for failing his test of fidelity, she takes shelter with Artemis, the goddess of the hunt.
After a while, Procris returns to charm her husband with two awesome gifts. Guess what they have to do with? Yup. Hunting. Procris gives Cephalus a dog that always catches its prey and a javelin that never misses its mark.
The end of the story keeps the hunting motif going strong: Procris dies in a hunting accident. Suspecting that Cephalus is out prowling around for more than just wild game, Procris hides in a bush to spy on her husband. Unfortunately, Cephalus thinks the rustling he hears is a beast and he hurls his never-missing spear, skewering his wife.
So why does a tale about two lovers torn apart by suspicion involve so many images and incidents related to hunting? Could it be a metaphor for love? (The Bachelor doesn't have a monopoly on that.) Cephalus and Procris are deeply in love with each other, but their distrust forces them to always be on the offense, ready to attack whenever necessary.