By the way, it's somewhat ironic that Nicene theology is accused of having been created under the influence of "Greek philosophy", when in reality, the CONTENT of Nicene theology was not influenced by any philosophy. They only utilized concepts found in philosophy to ARTICULATE the revealed truth. In contrast, subordinationism, and especially Arianism, had its specific content influenced by Greek philosophy.
Subordinationism is a speculative idea about the doctrine of the Trinity by some 2nd-3rd century Christian writers, and it is still closer to Nicene theology than to Arianism. They conceived of the Son and the Holy Spirit in some subordinate degree to the Father. They imagined the origin of the Son as the Father having eternally conceived His Word (Logos), but only pronounced it in creation (this is the so-called two-stage Logos theory). They were influenced by Greek philosophy in their speculation, which talked about different degrees of emanation from the divine. We must also consider that these pre-Arian theologians viewed the Son's subordination more from a soteriological-grace perspective, not on the plane of existence, meaning it only manifests in the created world, our world. Internal Trinitarian origins probably influenced them too. Anyone who is born or originates can somehow be considered lesser than the one from whom they originate. The clarification of concepts and theology only took place in debates with monarchians, Marcionites, and Arians when the Church Fathers recognized and articulated that the divine persons differ only in their relations to each other, not in their possession of existence.
Arius, moreover, mainly taught in Antioch, one of the contemporary centers of Aristotelian philosophy: Arius learned from Aristotle that a difference in name implies a difference in subject. The apple is not the tree, so the Father is not the Son. If the distinction between the apple and the tree were not real, both could be given the same name. On the other hand, if the Father and the Son must be distinguished by name from each other, it is obvious that they are not the same. For Arius, this meant that if the Father is God, then the Son cannot be God in the same sense. He can be divine, but his divinity is either partial or derived. (See Gerald Bray: Creeds, Councils and Christ—Did the early Christians misrepresent Jesus?, Rossshire, England, Mentor Books, 1997, p. 106)
Interestingly, Jehovah's Witnesses still argue against the Trinity using Aristotle's logic applicable to the natural world. The early church fathers, in any case, fought against polytheism just as strongly as they did against Arianism, seeing it as a variant of polytheism. Surprisingly, despite claims to the contrary, Arianism was closer to the philosophy of Plato and Gnostic speculations, not to Trinitarianism. The Platonic and Gnostic view does not tolerate the idea of God becoming man because they don't believe He can be related to the created material world. They believed that the "demiurge", a being between God and man, the first created "divine" being, created the material world which they deemed inherently evil. Against this, it was the Trinitarians who defended the ancient Biblical belief that only God Himself is the creator. It's also no coincidence that the late Roman emperors leaned towards Arianism, traditionally considering themselves semi-divine. It was much harder for them to accept Trinitarianism, which sharply separated the sole Creator from all other creatures.
Hence Arius' starting point was rationalist philosophy and speculation. The Antiochenes were followers of Aristotelian wisdom, mainly focusing on the interpretation of writings and preferring the literal meaning; they leaned towards rationalism. The founder of the school was Lucian of Antioch, a disciple of Paul of Samosata, and the teacher of Arius. Arius was an Alexandrian presbyter who, following in the footsteps of his teacher Lucian, the founder of the Antiochene catechetical school, forcefully asserted the unity of God in his work "Thalia" around 318.
According to him, the one true God (ὁ ἐπὶ πάντων θεός) cannot share His nature because He is simple; nor can He beget, because a begotten God is a contradiction. Consequently, the Son, who is a different person from the Father, was not born of the Father's essence but was made (γενητός, not γεννητός) by Him, a creation (κτίσμα) and came into existence from nonexistence (ἐξ οὐκ ὄντων ἐστίν); there was a time when He did not exist (ἧν ποτε, ὃτε οὐκ ἧν). But He was created before all "other" creatures, and God created through Him; thus, He is an intermediate and mediating being between God and the world; like the aeons that emanate from divinity according to the Gnostics, but Arius believed the Logos encompasses these non-worldly, non-divine aeons, the pleroma (cf. Col. 1:19).
So it was from this speculation that Arius derived his teaching, and only afterwards did he look for "evidence" from the Scriptures, such as Proverbs 8:22, ambiguously translated in the Septuagint.
Arius had two particular followers who sought to set up a theological system using Aristotelian dialectics: Aetius of Antioch and Eunomius of Cyzicus. They regarded being unoriginate as a divine basic property and applied it only to the Father. This implied that the Son and the Holy Spirit, having their origin in the Father, could not be coequal with Him, but are mere creatures. They didn't consider what the Western fathers emphasized from the beginning: that being unoriginate refers to the divine essence itself, which all three persons equally possess, and are one with it. The difference is only in the relations between the persons. The Son is begotten of the Father in such a way that the Father communicates his entire essence to him, not in time or sequentially, but in eternal existence.
The Father is the originless (unbegotten) primal principle in divine life; the Son is born from Him. But this begetting and birth should be conceived in the eternal, unchanging spirit. Insofar as the Son is also the Word, the Logos, His birth from the Father should be thought of in the image of expressing a word. The Father has known Himself eternally; there is nothing in His essence that He does not grasp, hence He can express Himself in a single, eternal Word such that the Word remains in Him and fully reflects Him. Yet He is the expresser, and the Son is the expressed Word. But because this expressed Word is the perfect image of the Father and contains the entire divine essence, its derivation can be called birth. Since cognition is the work of the intellect, we can say that the birth of the Son comes about through intellectual activity.
God Himself is life and activity, but nothing new arises in Him; He cannot change. But if the Son is His Word, coeternal with Him, then He surely expressed Himself in Him. He encapsulated His entire essence in this word, for as an infinite spirit, He fully knows and can express Himself. The expressed word, therefore, is consubstantial with Him, remains in Him, yet stands opposed to Him, like the expressed stands against the expresser, like the Son stands against the Father. Thus, the persons are distinguished only by their opposition in origin, but the divine nature or essence is not divided by this. The Father thus begets the Son, sharing His entire essence with Him, rather than giving something of Himself.
To understand the reality of the persons, attention must also be paid to the relation, the relationship between them. In created things, relationships arise subsequently: a man becomes a father when he has a son, and this fatherhood is accidental, not identical with essence. However, God did not first exist and then subsequently beget the Son; instead, He has from eternity, as He necessarily knows and expresses Himself. In the Trinity, the real mystery is that in the Father, the relation referring to the Son is not accidental, but intrinsically identical with the essence. Here we encounter an "existing relation," and in this lies the reality of the persons. Fatherhood as a relation faces sonship, therefore differs from it, yet neither differs from the divine essence itself, so the distinctness of the persons does not divide the unity of the Godhead. Thus, we encounter the wonderful unity and richness of absolute existence and relative existence, which does not occur in the created world.