Conference and difference opposites? [closed]

I am reading a book where diffidence and confidence were juxtaposed. In a later sentence, I noticed the word difference also has this same dif- prefix that diffidence does. Does it make sense to juxtapose it with conference in the same way? If so, what do the prefixes con- and dif- mean? What does ference mean?

Speculation: A difference is something that things don't have in common. A conference can be framed as an event where people come together to share something they do have in common, like an interest in comics or a certain hobby, so it seems reasonable to assume this meaning was derived from "conference: something that things do have in common".

Just because two prefixes are opposite in meaning and are both added to the same root, it does not follow that the two words thus obtained are antonyms.

The prefix in difference is dis- which was assimilated by doubling the first vowel of the Latin verb ferre. Etymoline says that this word dates from:

mid-14c. from Old French difference "difference, distinction; argument, dispute" (12c.) and directly from Latin differentia "diversity, difference," from differentem (nominative differens), present participle of differre "to set apart," from assimilated form of dis- "apart, away from" (see dis-) + ferre "to bear, carry".

About the prefix dis-, Etymoline says that it is:

word-forming element of Latin origin meaning 1. "lack of, not" (as in dishonest); 2. "opposite of, do the opposite of" (as in disallow); 3. "apart, away" (as in discard), from Old French des- or directly from Latin dis- "apart, asunder, in a different direction, between," figuratively "not, un-," also "exceedingly, utterly." Assimilated as dif- before -f- and to di- before most voiced consonants.

Con- is also a Latin prefix:

word-forming element meaning "together, with," sometimes merely intensive; it is the form of com- used in Latin before consonants except -b-, -p-, -l-, -m-, or -r-. In native English formations (such as costar), co- tends to be used where Latin would use con-.

It is true that these two words, conference and difference were both formed from the same root (the verb ferre - to bear, carry), but I don't see how they could be presented as opposites (unless you establish an artificial antonymy between them, like a pun of words).

In fact the meaning of bringing people together in conference (as a meeting, physically being together) is quite different from the meaning of "bringing people asunder" in difference (in opinions or characteristics): Conference can bring together very different people, and it does not necessarily imply consensus. If you look up the word conference you will not find that it is connected to the idea of unity of opinion. It is an event, and an event cannot be the opposite of a feature.

This is not a case of antonymy as it happens with consensus and dissensus.