Plurale tantum (plural-only nouns, like trousers or scissors)

It seems to be mostly a thing for objects where you can't lose 50% of it without it becoming something rather different to the pair. For instance, 50% of a pair of scissors is a knife, and 50% of a pair of glasses is a monocle. But if you lose one shoe from a pair, the other one is still just a shoe.

On a side note, a pair of scissors would be ideal for splitting a pair, were you ever in need of a single trouser!