The Dunedain

[Voralphion]

considering he told elrond that he didnt want the kingship.

Aragorn not wanting the kingship was only in the movie, not the book.
I believe the reason that Aragorn never claimed the kingship of Gondor was because he knew that Gondor was at war with Sauron and didn't want to weaken the strength of the city by starting off more kin-strife. He knew he had to wait until Sauron was defeated and for him to do great deeds in the war before bringing his claim to the throne.