I do not think Arwen was being irrational. Because, forever is a long time to spend alone. And, also, you must keep in mind that perhaps they were together once they both passed. So, if Arwen hadn't done that, then, (because of her being an Elf and all) she wouldn't have died. So, they could never be together in death, also. At least with giving up her immortality she got to spend a little time on earth with him. And personally, I believe that in death they were together. So, this was acheived by her giving up her immortality.
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