Analysis of ἀπόλλυμι:
We'll analyze the Greek word translated as "perish" first. The word is ἀπόλλυμι (Strong's G622), pronounced apollumi. Its primary meaning is "to destroy", "to kill", "to perish", "to lose (one's life)", "to demolish" or "wipe out". Essentially, it refers to the termination of life, and this is how it is mainly used in the New Testament (e.g. Matt. 2:13; 8:25; 10:39; 12:14; 16:25; 21:41; 22:7; 26:52; 27:20; Mark 3:6; 4:38; 8:35; 9:22; 11:8; 12:9; Luke 6:9; 8:24; 9:24, 25; 11:51; 13:3; 5; 33; 15:17; 17:27; 29; 33; 19:47; 20:16; John 6:39; 10:10; 11:50; 12:25; 18:14; Acts 5:37; 1 Cor. 10:9, 10; 15:18; 2 Pet. 3:6; Jude 5; 11), as well as in the Septuagint (e.g. Gen. 18:28; 19:13; 20:4; Exo. 19:24; Lev 26:38; 41; Num. 16:33; 21:29, 30; Deut. 4:6; 8:19, 20; 11:4; 17; Josh 11:14; 23:13; 2 Kings 10:19; 13:7; Job 3:11; 4:9; Psa. 9:3; 5; 49:10; Isa 13:9; 11; 14:20; 22; 25; 34:2; 60:12; Jer. 44:12; 46:8; 48:8; Ezek. 28:10; 31:17; 32:12, 13; 33:28; Dan. 2:12; 18; 24; Zeph. 2:5; 13). However, ἀπόλλυμι can have other meanings than dying/killing. In traditional interpretations of John 3:16, it is purported that the word carries with it one of these alternative denotations, rather than the usual meaning of "to die". Would such an interpretation have any basis? Before that, let's examine the other meanings of ἀπόλλυμι.
The occurrences of ἀπόλλυμι in the NT where the word definitively refers to something other than perishing or being destroyed are Matt. 5:29, 30; 10:42; Mark 9:41; Luke 15:8, 9; 21:18; John 6:12; Acts 27:34; 2 John 1:8, where it refers to losing an item such as a body part, a reward, a coin, or a piece of food, Matt. 9:17; Mark 2:22; Luke 5:37; John 6:27; 1 Pet. 1:7, where it refers to things such as food, gold, or wineskins being physically ruined such that they are unusable or worthless, Heb. 1:11; Jas. 1:11; Rev 18:14, where it refers to something passing away or perishing such that it no longer exists, such as the beauty of a flower when it withers, the heavens and earth, or the luxuries of Babylon, and 1 Cor 1:19, where it refers to the supposed wisdom of those in the world who are considered by themselves and by others to be wise and knowledgeable being proved by God to be fraudulent and counterfeit; a perverted simulacrum of authentic wisdom.
Defenders of eternal conscious punishment (ECP) mainly utilize Matthew 9:17, Mark 2:22, Luke 5:37, and John 6:27 to support their doctrine. Just as a reminder, the doctrine teaches that whenever the Bible refers to the final destruction of the wicked, it is referring to them being banished from God's presence whereupon they will endure some form of physical and/or spiritual torment for eternity in everlasting bodies (not as disembodied spirits, but as living, material beings); basically, the final judgement of the iniquitous is one where they are separated from God and His love and remain alive forever in torment. This is what they would have ἀπόλλυμι refer to in John 3:16. Do the verses above allow the word to carry such a meaning in John 3:16? No.
First off, traditionalists say that as the wineskins or food are ruined and made worthless, so the wicked in hell will be. I'm not sure how this translates to them remaining alive forever separated from God in torment. That doesn't follow. Not to mention that in the verses above, the wineskins and food are physically (not spiritually) ruined. The wineskins exploded and all the wine poured out, and food rots and decays, even to the point that it has fully decomposed. Imagine anything like that happening to a human. You would not think that they would stay alive forever conscious, would you? But according to the doctrine of ECP, those in hell do, and the sort of ruination they experience is not the physical kind that the wineskins or food undergo, but spiritual in the sense that they are deprived of all love from God and left purposeless. But ἀπόλλυμι is not at all used in such a manner in the given verses, all this notwithstanding that the word refers to inanimate objects, not living entities like humans.
In almost all of the instances in the NT where the subject of ἀπόλλυμι is a living being such as a person, it unequivocally carries the meaning of death and destruction, the kind whereby the organism's life ends. There are no instances where it conclusively does not refer to death when the subject is a person. Some point to Luke 15:24; 32, Romans 14:15, and 1 Corinthians 8:11 for examples of this. But these verses are not indisputable examples of such a use of ἀπόλλυμι. The latter two verses can be interpreted as saying that we "destroy" our fellow brother in the sense that we, through our actions, cause them to lose faith in Christ, the one who died for them, and be condemned to destruction. Of course, it could also be talking about making our brother spiritually frail or weakening their faith, rather than causing them to lose salvation. The verses are not unambiguous.
And as for Luke 15:24; 32, you may think that this one is definitive, as the prodigal son did not die. While that's true, had he not returned to his father, he would have. A terrible famine had arisen (v.14), and the son had become malnourished and was starving (v.16-17), which is why he saw no choice but to return to his father, because he knew what awaited him if he did not, namely, death. So, the son, in being "lost" (ἀπόλλυμι), that is, separated from his father, was doomed to die. This is one of the points of this parable (as well as the one in verses 3-7 of the same chapter, as sheep without a shepherd cannot survive, cf. Ezekiel 34:1-8); without God, we are destined to perish, as only He can sustain our lives. Hence, ἀπόλλυμι in Luke 15:24; 32 is not disconnected from the concept of dying.
To conclude, based solely on an analysis of the meanings and usages of the word ἀπόλλυμι, it is highly implausible that the word means anything other than physically perishing in John 3:16. We established that the predominant use of ἀπόλλυμι is to denote death, that is, the loss of life, especially when the subject is human beings.
Whenever it has a different meaning such as "to be ruined" or "to pass away", it is with reference to nonliving entities and not sentient organisms like humans, though even if such a meaning were to be present in John 3:16, it is certainly more likely to signify the destruction (privation of life) of those condemned than of their severance from God whereby they are rendered without purpose and remain for eternity in torment. In fact, such a use of ἀπόλλυμι cannot unambiguously be found anywhere, not in the New Testament, the Septuagint, or in any extrabiblical literature. However, the meaning of "perishing" or "killing" is found abundantly.
And finally, even in the rare instances where ἀπόλλυμι does not unequivocally mean the death of a person despite them being the subject (Luke 15:24; 32, Rom. 14:15, and 1 Cor. 8:11), it may still be interpreted to carry with it the notion of dying, especially in Luke 15:24; 32, where the son being "lost" meant that he was going to die from hunger. But we have yet to consider the most important factor in determining the meaning of ἀπόλλυμι in John 3:16, namely, the context of the verse.
Analysis of the context:
[John 3:14-17] And just as Moses lifted up the serpent in the wilderness, so must the Son of Man be lifted up, 15 so that everyone who believes will have eternal life in Him. 16 “For God so loved the world, that He gave His only Son, so that everyone who believes in Him will not perish, but have eternal life. 17 For God did not send the Son into the world to judge the world, but so that the world might be saved through Him. (NASB)
John starts off by alluding to the bronze serpent that Moses lifted up in the wilderness, and analogizes that account to the Son of Man being "lifted up", because everyone that believes in Him "will not perish, but have eternal life". John typifies the episode at Numbers 21:4-9, meaning it prefigures the Son of Man being elevated upon the cross. How does it do this? Several ways. First, it symbolizes the love and mercy of God that is encapsulated within Christ's death on the cross.
In Numbers 21, the Israelites, while on a journey around the land of Edom, had become impatient and started to speak against Yahweh and Moses (v.4-5), and so as punishment, God sent serpents to bite the people so that they would die (v.6). But the people had repented (v.7), and so, in an act of grace, God provided a way for them to be delivered from their judgment, which is the death that would have been inflicted upon them by the snakes. He told Moses to make a bronze serpent and lift it up on a pole so that all who gazed upon it would live and avoid dying from the snakebites (v.8-9). And so it is with the Son of God.
Because of our sin, we are worthy of death, and thus God would be just to inflict that penalty upon us. Negligence and violation of God's commandments engenders death (Gen. 2:16, 17; 3:17-19; Rom. 1:28-32; 6:21-23; 8:13; Gal. 6:8; Jas. 1:15). Indeed, sin is a fatal illness, but thankfully, God has provided a cure. Though we have merited judgment, God, in the boundless love and mercy that is intrinsic to His character, has provided a way for all those who are remorseful at heart to escape the rightful consequences of their sin in His Son. This is what John 3:15-17 says; "everyone who believes will have eternal life in Him... for God so loved the world that He gave His only Son... so that the world might be saved through Him". God gave humanity His Son as a means of salvation, so that we may be delivered from judgment, as the Israelites were.
Of course, like them, we must be repentant and have faith in God. They regretted what they had done and asked Moses to pray to God because they trusted He could save them. All who beheld the bronze serpent did so because they had faith that God could rescue them from death. And so we repent and trust in Jesus, in His death on the cross, and that He alone can save and redeem us.
And might I point out that the death the Israelites would have experienced due to the snakebites was ordinary death, i.e. the cessation of life. It was not separation from God and His love nor torment of any kind. Hence, there is no reason to think that the perishing John speaks about is qualitatively divergent from the perishing the Israelites endured, such that it actually means living for eternity in torment and separation from God, never to die. Such a notion is found absolutely nowhere in the context, and it would be absurd to impose it, especially when John had just reminded us of the account in Numbers 21, where the only death that occurred was the physical kind.
The only difference between the life and death in Numbers 21 and the life and death we receive based on whether or not we believed in God's Son is a quantitative one; in the former, the life and death are temporary, while in the latter, they are they are permanent and unending. There is no indication of a qualitative difference, especially not one as major as the one suggested by ECP proponents, where those who perish actually live forever in hell. Indeed, the comparison would lose most of its force and appear even ridiculous. And so, taking everything we have discussed into account, it is unreasonable to say that "perish" in John 3:16 denotes anything other than dying, i.e. being deprived of life.