Why do only people from the Uzumaki Clan get chosen as the Jinchuuriki for the Nine-Tails? Up until now, only people from the Uzumaki clan were shown to host the Nine-Tails:


Mito Uzumaki
Kushina Uzumaki
Naruto Uzumaki


were all shown as the Jinchuuriki for the Nine-Tails.

Why can't people from other clans be hosts of the Nine-Tails?
The answer pretty much lies on the skills and abilities of the Uzumaki Clan.

1st: Members of this clan were very knowledgeable in the art of fūinjutsu, and were both respected, and feared worldwide because of their prodigious skill. Fūinjutsu are a type of jutsu that seal objects, living beings, chakra, along with a wide variety of other things within another object. Fūinjutsu can also be used to unseal objects either from within something or someone.

2nd: The Uzumaki Clan lives in Uzushiogakure. The people of Uzushiogakure were noted to have notoriously long lives, so it gained the epithet "The Village of Longevity". The clan's life force was the reason Kushina survived the extraction of her tailed beast, despite additionally just giving birth only moments before, though she was left severely weakened.

These two (as far as I know) are the reasons why they are a chosen to be jinchuriki.

And another thing, if you analyze the situation, as the parent or member of certain clan that possesses a Kyubi, it is more likely for them to give the Kyubi as an inheritance for the next generation (Ex: Kushina to Naruto: given also the fact that they have the required skill to do that)

Sources:


Uzumaki Clan
Uzushiogakure