Arwen was not an Elf (see Letter 345 for JRRT say this specifically). She was a Peredhel as was her father and grandparents on her fathers side (etc). Until she made her choice she merely lived with the 'youth of the Eldar' (see App. A). Even after she made her Choice she was not a Man any more than she was an Elf before. She remained a Peredhel, whose ultimate fate was that of mortals.
The only way any of those with mixed blood were granted a Choice was if Manwe allowed it (or granted some other Doom). Otherwise they had the fate of Men.
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Tar-Elenion
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