Let us investigate.

The modern Greek word "αντικείμενο" (an-tee-KEE-meh-no) ≈ "object, subject" as in a physical object, a grammar object, a computing object, etc.

Aristotle in his writings on logic and reasoning and refuting bad reasoning will often use this Greek word in the sense of "opposite".
English: To sum up, in dealing with arguments which turn on language the solution will always depend on the opposite of that on which the argument turns. Loeb Classical Library, Vol. 400, p. 117.
Greek: Ὅλως δ´ ἐν τοῖς παρὰ τὴν λέξιν λόγοις ἀεὶ κατὰ τὸ ἀντικείμενον ἔσται ἡ λύσις ἢ παρ´ ὅ ἐστιν ὁ λόγος. Sophistic Refutations 23.1.

More: Eristic reasoning creates strife and contention

Consider the phrase "in opposition" that may mean "opposite" or it may have the additional idea of "adversarial".

The Greek word for "opposite" was usually translated in the Latin Vulgate as "adversary" which influenced later translations.

The English word "adversary" comes, through French, from the Latin word "adversarius" ≈ "opponent, adversary, enemy" which comes from the Latin word "adversus" ≈ "set opposite, turned toward".

An "adverse" situation is a situation that is "opposite" to another situation. One tends to focus on the "unfavorable" situation which leads to the general meaning over time.

Here, the Latin "adversaries" were "opposites" to Jesus and, by inference, those who were "opposite" to his views. They were "adverse" or "opposite" to his sayings.

The Old Church Slavonic word "стыдяхуся" ≈ "opposing".

The Russian word "противившиеся" ≈ "opposed".

There are many "opposite" to Paul.
In general, anyone opposite to one's point of view might be considered an "adversary". What about an "opposite" to an "opposite"? Logically, an "opposite" to an "opposite" (when there are more than one) may still be an "opposite".

In more precise logical terms, the relation of transitivity may not hold in the presence of negation.

Details are left as a future topic.

What is the "opposite" to an "opposite"? Ancient proverb: The enemy of my enemy is my friend. Used by Churchill in his decision to ally with Stalin against Hitler.

The "flesh" and the "spirit" are "opposites" rather than "adversaries" which is the Latin word used here.

The KJV sounds like the "adversaries" are an external threat. Throughout his letter to the Philippians, Paul is warning against the empty opinion and false reasoning of the "bishops" (leadership). Thus, the "opposites" are an internal threat.

The Greek for "terrified" is a word made up by Paul and, by parts, means "remain as spit" as the "opposites" take advantage of the true believers. To the "opposites" the humbleness of the true believers is a sign of the "destruction" of those true believers by the "opposites", but that is not so.

The one who "opposeth" Christ is he who is "opposite" to Christ. This leader mentioned by Paul is often taken to be the "antichrist". The Greek prefix "anti" means "instead of" so the "antichrist" is not someone who "opposes" Christ but sets himself up "instead of" Christ or "as" Christ.

More: The one Antichrist and many antichrists

More: The prefix anti in place of against

Those who are "contrary" to sound doctrine are those who are "opposite" to sound or "healthy" doctrine or "teaching".

More: Teaching and learning sound and healthy doctrine

More: Didache: The doctrine of teaching

Which word fits better?

• Who is the "adversary"?
• Who is the "opposite"?

Might this be an external threat from outside the family or an internal threat from inside the family (or both or neither)?

The Greek for "speak reproachfully" has to do with "speaking against" but without purposeful reason. The ancient Greek word "λοιδορέω" ≈ "abuse, insult, revile". The Greek for "occasion" has to do with "pretext" or "cause" and comes from the words for "from" and "attack".

The Greek for "favor" or "joy" here is an example were a "favor" may not be perceived as "good" or "joy".

A paraphrase: Do not give the opposite the pretext as a favor or joy of verbally abusing or insulting you.

What "things" might these be? Could they be "opposites"?

Might the "enemies" be the "opposites" to those not on the side of the Lord?

There is another Greek word that is often translated as "adversary" with a meaning of "accuser" based on the Latin word (and not the Greek word).

The Greek word for "quickly" is the same Greek word that in Revelation is often translated as "soon" as in "Jesus will come soon" rather than "Jesus will come quickly" as in this verse "at any time".

More: Come quickly: sooner or later

The modern Greek word "αντίδικος" (an-TEE-thee-kos) ≈ "legal opponents".

The modern Greek word "αντιδικία" (an-tee-thee-KEE-a) ≈ "litigation".

How well does "accuser" fit instead of "neighbour" in the following verse?

KJV:
LXX (Septuagint): Brenton Septuagint