That is fallacious reasoning; the etymology does not determine the meaning of a word, usage does. And the claim is incorrect on its face....the prefix arkh- does not imply a unique referent. It frequently designates an office or class that is ranked over others. For instance, arkhiereis "chief priests" in Matthew 2:4, 20:18, 21:15 is in the plural and definitely does not imply that there was only one "chief priest". Furthermore the word arkhaggelos occurs only twice in the NT and was not a Christian neologism; the word originated in earlier parabiblical literature of the Second Temple period (as it is absent in the OT). So in order to understand the meaning of the term, we must look to those pre-Christian and non-Christian parabiblical writings, as well as how the term was used in Christian literature. This is particularly obvious since one of the only two instances of the word in the NT occurs in an allusion to a noncanonical book (the Assumption of Moses). We can readily see that arkhaggelos was frequently pluralized and there were others named as archangels aside from Michael:
"And on hearing this, the four great archangels (hoi tessares megaloi arkhaggeloi) Michael, Uriel, Raphael, and Gabriel looked down from the sanctuary of heaven upon the earth and saw much bloodshed upon the earth. All the earth was filled with the godlessness and violence that was done on it. And entering in, they said to one another, 'The spirits of men grown, making petition saying, "Bring in our judgment to the Most High" '. And approaching, the four archangels (hoi tessares arkhaggeloi) said to the Lord, 'You are the God of gods and Lord of lord and King of kings and God of men' " (1 Enoch 9:1-4; translated from Aramaic in the second or first centuries BC).
"These are the names of the holy angels of the powers: Uriel, one of the holy angels, who is in charge of the world and Tartarus, Raphael, one of the holy angels, who is in charge of the spirits of men, Raguel, one of the holy angels, who pursues the world of the luminaries, Michael, one of the holy angels, who has been put in charge of the good ones of the people and over chaos, Sariel, one of the holy angels, who is in charge of the spirits who sin against the spirit, Gabriel, one of the holy angels, who is in charge of Paradise and the serpents and the cherubim, and Remiel, one of the holy angels, whom God has put in charge of those who will rise. These are the seven names of the archangels (arkhaggelón onomata hepta)" (1 Enoch 20:1-8).
"I, Jacob, who is speaking to you, am also Israel, an angel of God and a ruling spirit.... And when I was coming up from Syrian Mesopotamia, Uriel, the angel of God, came forth ... and envied me and fought with me and wrestled iwth me saying that his name and the name that is before every angel was to be above mine. I told him his name and what rank he held among the sons of God: 'Are you not Uriel, the eighth after me [i.e. not of the seven archangels], and I, Israel, an archangel of the power of the Lord (kagó Israél arkhaggelos dunameós kuriou) and chief captain among the sons of God?' " (Prayer of Joseph 1, 4-7; written in the first century AD).
"The most eminent Babylonians and Hostanes and Zoroaster authoritatively call the heavenly spheres 'flocks', either in so far as alone among corporeal magnitudes, they are completely drawn around a single center, or because their connections are decreed even by scientific savants to also in a sense be called 'clusters', and they for the same reason call these clusters 'flocks' in their holy writings, and also 'angels' by insertion of the lost 'g' [i.e. agelos 'flock' and aggelos 'angel']; hence the heavenly bodies and spirits which are outstanding in each of these flocks are likewise called angels or archangels (arkhaggelous), and these are seven in number (eisin hepta ton arithmon)" (Nicomachus, Theologoumena Arithmeticae, 57.8; written in the first century AD).
"But even Michael the archangel (Mikhaél ho arkhaggelos), when he was disputing with the devil about the body of Moses, did not dare to bring a slanderous accusation against him, but said, 'The Lord rebuke you!' " (Jude 9; written in the first century AD, a reference to the book Assumption of Moses).
"Adam lay for three hours and then the Lord of all, sitting on his holy throne, stretched out his hands and took Adam and handed him over to the archangel Michael (tó arkhaggeló Mikhaél), saying to him, 'Take him up into Paradise, to the third heaven, and leave him there until that great and fearful day which I am about to establish for the world'. And the archangel Michael (ho arkhaggelos Mikhaél) took Adam and brought him away and left him...And he spoke to the archangel Michael (tó arkhaggeló Mikhaél), 'Go into Paradise in the third heaven and bring me three cloths of linen and silk.' And God said to Michael, Gabriel, Uriel, and Raphael, 'Cover Adam's body with the cloths and bring oil from the oil of fragrance and pour it on him.' And thus they did and prepared his body ... Then the angels took up the body [of Abel] and set it on the rock, until the time his father died, and both were buried according to the command of God in the regions of Paradise in the place from which God had found the dust" (Greek Life of Adam and Eve 37:4-40:6; written in the early second century AD).
"First, Gabriel was revealed [to Mary] in his strong and holy person. Second, the archangel (arkhaggelos) [i.e., Gabriel] also addressed the maiden in speech" (Sibylline Oracle 8:459-460; written in the late second century AD, c. AD 175).
"And who can enumerate one by one all the remaining objects which have been constituted by the power of God, and are governed by His wisdom? or who can search out the greatness of that God who made them? And what can be told of those existences which are above heaven, and which do not pass away, such as angels, archangels (arkhaggeloi), thrones, dominions, and powers innumerable?" (Irenaeus, Adversus Haereses 2.30.3; written in the late second century AD).
"Neither worship as the Jews; for they, thinking that they only know God, do not know Him, adoring as they do angels and archangels (arkhaggelois), the month and the moon. And if the moon be not visible, they do not hold the Sabbath, which is called the first; nor do they hold the new moon, nor the feast of unleavened bread, nor the feast, nor the great day....And God is far from calling aloud in the unapproachable sanctity, separated as he is from even the archangels (arkhaggelón)" (Clement of Alexandria, Stromata 6.5.41, 6.7.57; written in the late second century AD).
"The righteous shall obtain the incorruptible and unfading kingdom, who indeed are at present detained in Hades, but not in the same place with the unrighteous. For to this locality there is one descent, at the gate whereof we believe an archangel is stationed with a host (ephestóta arkhaggelon hama stratia)" (Hippolytus, De Universo, 20; written in the early third century AD).
"The priests are analogous to the archangels in heaven (tois en ouranó arkhaggelois) turned toward the gods, of whom they are the messengers" (Porphyry, In Platonis Timaeum Commentaria, 1.17.5; written in the third century AD).
"As I was praying to the God of heaven and earth, there was granted to me from the Lord Sabaoth through Michael the archangel (dia Mikhaél tou arkhaggelou) a ring which had a seal engraved on precious stone....I prayed that Uriel the archangel (Ouriél tou arkhaggelou) would come to help me" (Testament of Solomon 1:6, 2:7; written in the third century AD)
"He was a chief captain of the power of the Lord which ... he recognized while doing service in the body, being reminded of it by the archangel Uriel (tou arkhaggelou Ouriél)" (Origen, Philocalia Sive Ecologa, 23.19; alluding to the Prayer of Joseph, written in the third century AD).
"When the captivity of the Jewish people at Babylon was near its end, Gabriel the archangel (Gabriél ho arkhaggelos), one of the holy ministers of God, appeared to Daniel as he prayed, and told him that the restoration of Jerusalem was to follow without the slightest delay, and he defines the period after the restoration by numbering the years" (Eusebius, Demonstratio Evangelica 8.2.5; written in the early fourth century AD).