Hopefully this will give some context for the rest of the story. I'm too lazy to explain the rest of this shit until later in the story so here you go you heathens. Enjoy. Or don't.
Generations ago, Inuzuka Kagura made a pact with a spirit of the forest when he came upon a dying wolf-dog and her pup. With a pact sealed in the blood of a mother, Inuzuka Kagura became the new guardian of a single living pup named Sojimaru. The forest spirit who witnessed this pact bound them by rite of blood and bone. Eventually beast became more akin to man and man slowly found himself a beast. Together they went on to achieve things no one thought possible and brought prosperity to their clan.
So it is with every Inuzuka that if they find a partner, a ninken who matches their soul, and with training and effort they too can reach that same resonance. When a child finds that ninken, that pup that can train and live with them as their companion, they receive their markings. This frequently happens before the fifth birthday and is a rite of passage for many Inuzuka.
However, when that same beast blood runs too strong in Inuzuka veins it leads to offspring that are more beast than man. These children, called Inu, inevitably give into those baser instincts. Legend has it that they shed their skin and leave their humanity behind, eventually becoming creatures of the forest. These children are blessed by the spirit who bound Sojimaru and Kagura, given their fangs before their birth.
This is why the Inuzuka have oftentimes looked outside of the clan, even outside of the village for mates, diversity means safety. If a child is considered too dangerous, they are frequently left in the forest, at the spirit's shrine, to die. Their bodies taken by the forest spirits to a land where monsters roam.
Kairi was proud to be born with her fangs. Proud to be the first Inu in several generations to survive infancy in Konoha. Her mother had been too weak to give her only daughter, the reminder of a love lost, over to the forest. Kairi had survived an invasion, a war, and the attack of gods, she was damn pleased to be an Inu