Witches

Is it true that magic is inherited from spirits to witches?

Not necessarily, no.

Magic does not require spirits whatsoever. Some people may choose to work with spirits or deities, and some may choose not to do so.

Magic is simply the influence of will on change, whether internal or external. It is not something which is inherited; it is a concept, and not an ability. Concepts are not genetic, nor otherwise hereditary or passed down. They are learned.