Seeking single word denoting a word pair in which one cannot exist without the other

Years ago a friend told me about word pairs in which one word cannot exist without the other word. The example he used was inside and outside. That is, inside cannot exist without its necessary other half outside.

At the time he told me a name for these word pairs, which I have long forgotten. What is the name describing these word pairs?

Consider complement

Either of two parts that complete the whole or mutually complete each other.

Similarly, counterpart

One of two parts that fit and complete each other.

both from American Heritage

Having two opposing concepts that are defined by each other is an example of yin yang duality which may be the word you're looking for.

Other than than, two words with opposite meanings are also antonyms or complementary to each other.

I think you are looking for binary opposition.

A binary opposition (also binary system) is a pair of related terms or concepts that are opposite in meaning. Binary opposition is the system by which, in language and thought, two theoretical opposites are strictly defined and set off against one another. It is the contrast between two mutually exclusive terms, such as on and off, up and down, left and right. Wikipedia

_{(emphasis mine)}

Deconstruction theory touches upon binary oppositions and explains how one of them cannot exist without the other:

Deconstruction is interested in the hierarchic binaries set up within texts. These could be: man/woman, speech/writing, white/black, inside/outside, full/empty, identity/difference, light/dark, presence/absence, similarity/difference. In each of these binaries, one term is privileged over the other. A deconstructive reading would show how, even when a text appears to privilege one term over the other (say, inside over outside), the text's logic of rhetoric reveals that there can be no inside without the outside. In other words, deconstruction shows how the less privileged term is central to the dominant term. By showing this centrality deconstruction reverses the hierarchy, for if the inside can exist only if there is an outside it means that the outside is the dominant element.

In its next stage, deconstruction destabilizes this reverse hierarchy too. It questions the new hierarchy and thus leaves even the displaced one unstable. Thus, the text remains unresolvable where neither term is privileged - a situation called 'aporia'.

_{Contemporary Literary And Cultural Theory: From Structuralism To Ecocriticism by Nayar}

_{(emphasis mine)}