Why do you 'think not'?
JRRT wrote it, and that is what he decided
Arwen did not have to make a choice until Elrond left (though she actually made her choice a couple dozen years earlier in Lorien. She was not an Elf. Luthien is noted as an 'absolute exception' among 'immortals' in being allowed to change her fate. Arwen was allowed to make a choice, not a change, and she had to choose between 'mortality' and 'immortality'. It is as simple (and complex as that).
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Tar-Elenion
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