Mythical creatures do not approach humans without a good reason to do so. Most of the time, humans are their preferred choice of prey. Otherwise, they might have a task that the human needs to perform. Sometimes, however, the human has very little to do with the decision at all. Even mythics grow old— and when they do, they seek out someone without magical potential in order to turn them into their heir.
In short, heirs are humans who have caught the attention of a mythic patron and have received a lineage from that mythical bloodline. Their life force is overwritten by the magical energies of the mythic, pushing their body into a "half-transformed" state. They take on physical traits reminiscent of their patron, and gradually receive their own mythical powers as the transformation takes hold. Then, when their training is complete, they receive the ability to transform completely into their mythic form— a change that will become permanent once their human lifespan reaches its end.
Once a human is chosen as an heir, there is no way to prevent the changes.
Heirs are fundamentally similar to witches, being one of the primary types of magic-users. The differences lie in the ways that their magic is manifested.
Heirs are primarily "internal" magic-users, who alter their own body with magical properties. They have a strong focus on spells and techniques that have been passed down by their patrons, but are encouraged to experiment with their abilities in their own time. It's also rather difficult for them to learn new techniques without outside assistance; an heir without a living patron is not going to get very far at all. Regardless, heirs are a sort of fixed point. They are better described as "half-mythics" instead of "half-witches," taking the role of something like an apprentice or a squire. If an heir's abilities are half-baked, it's not because they haven't studied enough— they are simply in a transitory state, waiting for their full powers to be unlocked at the end of their transformation.
And, of course, witches can never become heirs.