The nature of emotional relationships often overlaps in confusing complications ranging from the simple crush to Freudian oddness. If this causes the writers to accidentally build things like harems, the easy way to get around this is reveal the basal nature of a relationship.
In the character's mind, one type of relationship was simply confused with another. This has some basis in reality, where some potentially romantic relationships are actually people seeking "figures". (Hell, who hasn't done this at some point?) They spend time with a person because he or she reminds them of someone else. For example, some characters attracted to older characters often have an absent parent or older sibling or their dead little sister. This situation is often the inherent role of an Unwanted Harem's Unlucky Everydude.
In some other cases, it turns out that the character was only in love with the idea of being in love and applied it to the first suitable person they met.Doing this poorly can feel incredibly cheap if the "explanation" doesn't make sense or potential evidence wasn't presented beforehand, as it feels as if the writers are just going down the list of romantic opposition and checking them off.
Like Death of the Hypotenuse and Ron the Death Eater, this trope serves as a subtrope of Die for Our Ship in fanfic, to clear the way for the author's preferred 'ship.
If a character is Really 700 Years Old, this can keep the writers from having to deal with a Mayfly December Romance.
The trope name and quote refer to Éowyn's unrequited love for Aragorn from the Lord of the Rings trilogy. Accordingly, compare and contrast with All Love Is Unrequited. Not to be confused with Fighting a Shadow.