Being immortal, elves attempt to be preservers - they try to halt change as much as possible. Change can even give men turmoil in our short lives, so it wears and tears even more on elves as they live thousands of years. In Aman, they may rejoin their kin and live in a place that changes very little.
Elrond's concern for his daughter is different, as noted by the others before me. I wrote a full explanation of Elrond and his family's mortal/immortal situation
here. Simply put, they are half-elven (on each side of their family tree is the union of a man and elf). His family did many great things, and as their ancestors, he and his parents, brother, and children have the choice - mortal or immortal. He chose immortality, and his children have to make their decision before he leaves (or very shortly after).