Personally, I think a better question to ask is why do we want to depict the mentality of non-human species as significantly different from that of humans? There are many possible answers to that question, and they all point to different ways one ought to depict those species in order to achieve different goals.
For me, the answer is that alien mentalities can help hilight something interesting about human mentality by exaggerating it. Immortal elves are great for telling stories about grief, because their immortality burdens them with having to live to see everyone they once knew die, unless they isolate themselves from mortals completely, which can be viewed as analogous to pushing others away to avoid the pain of growing attached only to lose them. Elves can also serve as an effective representation of the time blindness experienced by folks with ADHD - an elf might struggle to manage their time because when you can live forever there is no real sense of time pressure. The temporal proximity to a future event can become abstract when the only real time-related categories you have schema for are “now” and “not now,” which can lead to things like important appointments and dates being completely forgotten.
Half-elves, on the other hand, serve a different allegorical role. Sure, they’re longer lived than humans, but in there case the purpose of that longer lifespan is not to explore stories of grief or time-blindness, but to reinforce their alienation from their peers. Too long-lived to fully empathize with other humans, too short-lived to fully empathize with other elves. As I’ve already gone on at length about in this thread, I see them as an allegory for the varied experiences of mixed-race individuals, and their lifespan and its effect on their mentality is in service to that allegory. Hence, the answer to the question of this thread of how they feel different from elves. They explore completely different facets of the human experience.