The Malfoys are part Dragon.
Long ago the Malfoys took pride in this and so it was considered common knowledge. But as the times changed it became...less fashionable, let's say, to be part Magical Beast.
And so they buried this fact.
Unfortunately Dragon Blood is not so easy to wash out, and so as much as they tried to dilute the Dragon Blood in their veins over the centuries, the Malfoys have had little to no luck and are just as Dragon as they were a thousand years ago.
But now, Wizards and Witches who are part Magical Beast are seen as, well...
Beasts.
Just look at how they treat Hagrid! How could they possibly let anyone know that they are part Dragon themselves?!
And so it is kept a carefully guarded secret in the Malfoy line, with every new family member married in being sworn to secrecy with an Unbreakable Vow.
Meanwhile, the ones with Dragon Blood in their veins... They are very careful to take advantage of their mixed blood as much as they can without exposing themselves.
For example, Dragons are naturals at Legilimency and Occlumency. And as such, so are Draco and Lucius Malfoy.
But there are negatives, too — or, perhaps "negative" is the wrong word, but they're definitely not useful and have high risk of exposing them as part Dragons. For example, Dragons purr and build hoards which they then obsess over.
Additionally, they cannot fly but they can breathe fire and are suitably fire resistant. Their Patronuses are always Dragons. They're territorial and are often quick to aggression even when unprovoked.
Etc.
