Abarim Publications' online Biblical Greek Dictionary
The noun θηριον (therion) is usually translated with beast or animal, and is used in the classics to describe any kind of wild animal, and especially those that were commonly hunted. It derives from the noun θηρ (ther), which also means animal, but which refers more broadly to anything that's not human, bird or fish (and in the classics this includes dolphins, boar, deer, and particularly lions).
The noun θηριον (therion) is technically a diminutive form of θηρ (ther), which in this case establishes an individual animal from the larger continuum of the "animal kingdom" that the latter word signifies (i.e. a therion is one of the ther). From this broader noun θηρ (ther) comes the German noun Tier, which indeed means animal (of any kind), and even the English word "deer", which describes a large ruminant mammal that distinguishes itself from similar animals in that it refuses to be domesticated and hence stays proverbially wild. And therein lies the rub.
The ultimate source of these words is the Proto-Indo-European root dheu-, meaning cloud or breath, whereas our word "animal" stems from the Proto-Indo-European root ana-, which means to breathe. Also note the similarity with the verb θερω (thero), to make warm (what a central fire does). Obviously, humans are animals too since both have breath (Psalm 73:22, Ecclesiastes 3:18, 2 Peter 2:12, Jude 1:10), and the sole difference between animals and humans is that the latter have civilization: speech, writing, technology, statecraft, arts, commerce, corporations and law.
Modern scientists very strongly suspect that the whole universe should be formalizable (i.e. spelled out) by one single theory, which they call the Theory of Everything. What that Theory of Everything might be is still a mystery, because the three great pillars of nature, namely gravity, quantum mechanics and life, are fiendishly difficult to unite. Still, and entirely likewise, very roughly and generally spoken, the God of the Bible can be defined as the oneness of all things. This may seem like a bumper sticker, but it's really a rather profound definition, particularly when we allow "all things" to include all living things plus all human minds (and even AI). It explains that God is love (1 John 4:8), and bears all things (1 Corinthians 13:7), and makes all things work together (Romans 8:28). The singularity from which the universe Big-Banged was never compromised, and since the oneness of all things is more fundamental than any- or all things, the oneness of all created things derives directly from the oneness of the Creator (which in turn implies that these two onenesses are in fact the same oneness, since you can't divide one oneness into two onenesses; all division belongs to nature).
The job of the entity known as the Word of God is to formalize the Creator (1 Corinthians 1:24, Colossians 2:9, Hebrews 1:3), and this Word thus describes both the oneness of the Creator and the oneness of all created things. This in turn explains the flowery statement that "Christ is incarnate in his people"; it means that all scientists, natural philosophers, non-religious theologians, original artists and other folks of "sound mind" put together would be able to verbalize the Theory of Everything, if they were only able to understand each other's languages and symbolic jargon. This is obviously a work in progress but we're slowly but surely getting there (Luke 2:40, 2:52, Matthew 11:12).
In the early 20th century, scientists were able to formalize that all created things derive from the oneness of all things; and not only all things but also all their governing forces and thus their interactions. This means that the oneness-of-God-and-of-creation is also what governs all goings on in the world. And since humanity diligently studies nature, and so gets wiser and more one, humanity is headed for the same oneness that makes both the universe and the Creator one, which will make humanity divine. All of this means that God is not only the past Creator, but also the present Governor and the future Objective of all things, both simpler than the singularity and more complex than the whole of the human mental and emotional sphere (Deuteronomy 6:4, John 17:21, Romans 1:20, Ephesians 5:27).
We moderns like to congratulate ourselves for being so very separate from the animals but that's a grim delusion. Without the 10,000 or so species of microbes that live within our bodies (that's about one microbe for every cell of "you" that has "your" DNA; about 1.5 kilograms of them per adult human), and which alter our moods and feelings, there would have been no human body. And similarly, without the dogs, cats, sheep, pigs, cows, horses, chickens and camels that live within our societies and do our work and give us food and clothing, and protect us and keep us company, there would have been no society. Without the wilderness in which our civilization sits (with its plankton, spores, vegetation, insects, winds, hydrological cycle and so on), our civilization would come to an end. Without space, there would be no earth. Without the oneness of all things, there would be nothing.
Wooly sheep don't naturally exist. Sheep the way we know them are human productions in the exact same sense that Michelangelo's David is a human production. Even though Michelangelo did not create the marble, his David is undeniably human. Likewise wooly sheep are as human as a song by Rihanna.
Humanity is not the tribe of naked apes we identify ourselves with, but the whole sphere of human cultivation (within and without our bodies) from which we derive our individual identity, and that includes gut microbes, marble statues, pop songs and domesticated plants and animals. Sheep don't sing songs or sculpt statues but neither do our microbes. Yet both our microbes and our sheep are essential in bringing about a world in which there are songs and statues. Both our microbes and our sheep benefit from what they would never comprehend, while neither could live without it.
Our modern English languages has no equivalent of the Greek noun θηριον (therion), because it doesn't simply describe a genetically non-human, but rather any creature that does not partake in humanity, does not understand the nature and width of humanity, and would destroy it for natural selfish gain without ever understanding what it had destroyed. The ancestors of our domesticated animals were never forced but showed up voluntarily to benefit from the relative safety of human camps. And that's because they desired what humanity desires. The nature of humanity, namely, is to seek the symbiotic oneness of all things, and the mission of humanity is to formalize the Word of God, so that all the intricacies, nuances and consequences of the oneness of all things can be easily taught to children.
The dynamics that govern every scene in the Bible draw from the Ten Commandments, and these Big Ten are two sets of rules, of which one talks about God (Exodus 20:1-8) and the other about humanity (Exodus 20:8-11). If we were to condense these Ten even further, the first set would become: "Love the Lord your God with you whole heart, soul and mind", and the second set would become: "Love you neighbor as yourself". These two rules govern the entire rest of the Bible (Matthew 22:37-40). If we were to condense these two even further, they would become one rule, namely: "Treat others the way you want to be treated". This single rule appears again somewhat as a bumper sticker, but it is really the most profound formal statement there is, and drives all dynamics in the Bible (Matthew 7:12).
This single "golden" rule is the most condensed version of the Word of God, and explains why all things are one. It explains the laws of conservation (of energy, momentum, baryon number, and so on) and ultimately even Noether's theorem. It explains consciousness, both self-consciousness and other-consciousness (a.k.a. Theory of Mind). And it even explains its own divinity and the reason for creation to exists, because when this rule exists but creation doesn't, the only way to apply (or "obey") this rule is to create something other (John 1:1-4, Colossians 1:16-17).
Long story short: without a dominant desire for the oneness of all things, a breather is θηριον (therion), and with it a breather is an ανδρος (andros). It's that very distinction and that distinction alone that governs the use of our noun θηριον (therion) in the New Testament — including the notorious "beasts" that John the Revelator mentions.
Our noun is used 46 times; see full concordance, and from it derives: