The average human requires some form of mental "Ending" to their inner-narrative's "Story Of My Relationship With This Person", AFAICT. Without some form of mental marker which can be officially labeled in their mind as the "End" of things, the person and their relationship with that person will linger in their subconscious and they will worry, stress and otherwise continue agonizing over the subject as when waiting to see if a disappeared or kidnapped person will come back or turn up dead eventually.

From my viewpoint, the need for "closure" is an extremely selfish desire for some external sign that they are allowed to stop worrying about it. However, for most people, it is a "natural" part of their life and the need for closure is socially accepted and often socially expected. Outside of LW, I would expect that qualifying a need for closure as "selfish" would earn me substantial scorn and negative judgment.