Board Thread:Chapter and Episode Discussions/@comment-4704473-20141106114903/@comment-25632268-20141106211443

FF-Suzaku wrote: The reason the Hyuga marry within their clan is to preserve their kekkei genkai. The byakugan therefore might be recessive, so without two Hyuga parents it's extremely rare. That's probably why the Hyuga are so strict.

And there is a very good example of Gaara's father - he had Magnet release as kekkei genkai and none of his children inherited it.