Elves were not always allowed to become mortal, it only happened twice. The first time was Luthien, the second time was Arwen. Although for Arwen, she was never a full elf as she hadn't made a choice as to what kindred she would belong to, so her choice to become mortal wasn't really giving up her immortality as it was only a temporary gift until she made the choice.
Also the comment that men were never able to become immortal isn't fully true either. Tuor, the father of Earendil, was able to become immortal after marrying Idril daughter of Turgon. That was probably also due to the fact he was chosen by Ulmo, but after going into the west he was granted immortality and counted among the elven race.
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His sword was long his lance was keen
His shining helm afar was seen
The countless stars of heavens field
Were mirrored in his silver shield
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