Abarim Publications' online Biblical Greek Dictionary
δεξιος
The adjective δεξιος (dexios) means right (the opposite of left) and is used 54 times in the New Testament; see full concordance. Particularly compared to the "left," the "right" has a decidedly positive connotation. In English we use the word "right" for things that are proper and just, whereas our word "left" hails from an ancient word that means "foolish." "Left" is also the homograph of the past tense and participle of the verb to leave, which is why it's not right to be left.
The Latins called the left sinister (hence our negative English word "sinister") and the right they called dexter (hence our positive word "dexterity," and of course the name Dexter). The Hebrews associated the right both with the south and with strength and alliance (hence the name Benjamin, or Son of the Right Hand), and thus the left with the north and weakness and hostility. The word for "right" in French is the same as our English word "adroit," meaning resourceful, whereas the French word for left also means clumsy or awkward. In English a clumsy person has two left hands.
But while the curious distinction between right and left cannot be denied, it's hardly a simple matter of good versus bad. In fact, the modern folkloristic distinction between right and left is rather clearly rooted in a very sensible ancient one. And it's that venerable ancient usage that is reflected in the Bible.
Goats to the left; sheep to the right
The rather curious distinction between the good right and the bad left appears to have made self-evident sense to pretty much everybody in antiquity, since it is incorporated in several broad language groups and that means it's a very old and pervasive idea. Our English word "left" may in fact have to do with an enormously ancient Proto-Indo-European root "laiwo-" which means "considered conspicuous," which also gave rise to the Greek word λαιος (laios), meaning left (not used in the Bible).
Some commentators suggest that these associations have to do with the directions from which invaders (lefties) and allies (righties) came but that makes little sense since alliances shifted often and invaders could come from anywhere. And even if invaders and allies consistently came from each their own direction, it's a huge leap to connect a geographic direction to one's own left or right side. The words left and right, after all, tell us something about things that are positioned relative to one individual observer (or, if you insist, several observers who all face the same way).
It seems much more logical that the right side and the left side became associated with certain qualities, or rather with the degree of practical usefulness of things, because most people are right-handed (about 90%). Particularly craftspeople would want tools that have a common and frequent use (say, a hammer) in easy reach of their right hand, and would position items that are still very useful but only on very special occasions (say, some nifty finishing tool) on the left.
From that same usage, rules and regulations that governed society's everyday life would evolve into common law (called das Recht in German, pravo in Russian, after pravo meaning "right"), whereas law that governed very special circumstances and required specialized legal experts, became associated with the nasty surprise of amateurs who erroneously thought they had it all figured out. It's precisely that moral ambidexterity that Paul refers to when he speaks of "the weapons of righteousness for the right hand and the left" (2 Corinthians 6:7). Quite similarly, when the mother of the sons of Zebedee asked for her sons to be seated one on the right and the other on the left of Jesus (Matthew 20:21) she imagined her sons to be both very useful, but one for everyday practical use and the other one for rare and specialized operations (actually, she asked for her sons to be seated one among those — plural — on the right and the other among those — plural — on the left; so that's not all that bad).
Without referring to right or left, Paul reflects on these same two kinds of usefulness when he mentions vessels for either common use or particular use (Romans 9:21), and similarly to vessels of gold and silver and others of wood and clay (2 Timothy 2:20).
And of course, we were told in Sunday school that we should all aspire to be very special golden vessels for the Lord alone to delight in, but that constitutes a whopper of an error. The Lord, who we are called to emulate (Philippians 2:5, 1 John 2:6), was a common worker from some obscure hamlet, who died the death of an uppity slave during a time when hundreds of thousands of uppity slaves were executed in the same way. Right after his remark about gold and silver vessels, Paul urges Timothy to be a vessel "for every practical use" (2 Timothy 2:21). That would be a wooden or earthenware vessel, kept handy on the right.
Folks who were wealthy enough to be able to withdraw from the hustle of common life, moved their social usefulness from the handy right to the elite left, where they began to specialize in less and less until they were experts in nothing at all. Those were, of course, the aristocrats, after the adjective αριστερος (aristeros), meaning left. Another much used Greek word for "left" is ευωνυμος (eunumos), which literally means "of good name," which is yet another euphemism for being so very special that one is only very rarely of any use.
In Christ, everybody is highly unique but the error creeps in when we begin to think that we're somehow better than others. The world finds it common to aspire to glorious functions, but where would any house be without a good toilet brush or a garbage can? To Jesus Christ becomes the greatest glory attainable to humankind (Hebrews 1:3, Jude 1:24-25) and he washed feet (John 13:5).
In Christ we are called to be as broadly useful as we can possibly be and not flaunt ourselves off as some kind of lofty elite clique (Romans 12:3). Jesus, after all, is positioned readily available at the right hand of the Creator himself (Matthew 22:44, Acts 2:33, 7:55, Romans 8:34, Ephesians 1:20, Colossians 3:1, Hebrews 8:1, 10:12, 12:2, 1 Peter 3:22).
Sheep and goats are both fine animals and there's nothing wrong with either. But where goats only yield milk and meat, sheep give milk, meat, wool and horns big enough to make trumpets from. Sheep are much more versatile than goats, and humans are called to be sheep, not goats. Folks who only mind their brethren from their own church and congregation are like goats, whereas people who clothe and feed people as indiscriminately as God himself (Romans 2:11) are like sheep (Matthew 5:47). It is for this reason that the Lord will reject these selective goat-people and accept the non-discriminatory sheep-people (Matthew 25:31-46).
δεξιολαβος
Our adjective δεξιος (dexios) comes with one derivative, namely the mysterious noun δεξιολαβος (dexiolabos), which is formed together with the verb λαμβανω (lambano), meaning to take. This noun appears to occur only once in the whole of extant Greek literature, and that is in Acts 23:23, where it describes part of the military contingent that was to guard Paul on his trip to Rome. Its meaning is subsequently unknown, but it obviously describes a kind of specific Roman soldier. What kind is anybody's guess, and many today believe it's a spearman. Why a spearman would be known as a right-taker is wildly unclear since swords, clubs and carrots are all held in the right hand of right-handed people.
Some Christian scribes of old solved this problem by swapping our noun for the equally unique word δεξιοβολος, from βαλλο, ballo, to cast. Spears were used for defense, however, and weren't meant to be cast, and a δεξιοβολος would be with the ballistics regiment (archers and stone slingers and all that). But a line of defense would logically be named after the shield, which was held in the left hand, so that doesn't work either.
Here at Abarim Publications we surmise that noun δεξιολαβος (dexiolabos) denoted a general-purpose soldier who was at the ready for all sorts of military activities, from running into battle to digging holes, peeling potatoes and escorting the occasional prisoner to his fate.