To further the thoughts of Raefindel and hobbitlass: Even if Aragorn died soon after becoming King, at least that would leave Arwen well-off, as the Queen.
But I think there was more to it, from Elrond's point of view. I think he knew that Aragorn was a decent man, but that he had not yet been "tested" -- in deep and challenging ways -- in his life yet. But by the time he had accomplished all of his Herculean Tasks, so to speak, he was an even better person: truly worthy of Elrond's daughter.
Note: I read somewhere that Elrond in some ways represented the priest who raised JRRT and his younger brother after their mother died. The priest, Fr. Francis, sternly opposed Tolkien's romance with Edith (future Mrs. Tolkien) because she wasn't Catholic. So Tolkien went to great lengths to convert the girl with whom he was madly in love so that he could marry the woman who was the inspiration for Luthien.
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- Eve
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