Why was homoousios used in the Nicene Creed?
The short answer is: The dogma of the Trinity was at stake!
Just because ὁμοούσιον does not appear in the Bible not in any other Creeds prior to Nicaea that the Nicean Creed should not be accepted! The entire creed has to be looked at as a whole.
In the two thousand years of church history Christians are continuously coming up with terms to express the various definitions of their faith. It is simply part of their organic development of trying to make clear their faith, in a logical well mannered way.
The word Trinity is equally not found in Sacred Scriptures either. But the vast majority of Christians are Trinitarians.
Another example is that the term "transubstantiation" was used at least by the 11th century to speak of the change in substances in the Holy Eucharist and was in widespread use by the 12th century.
Hosius of Corduba and not Constantine presided over the Council of Nicaea, as his name appears first on the list of participants.
Emperor Constantine eventually moved the convocation to the First Council of Nicaea which opened on 20 May 325. Hosius probably presided over it, as his name appears first on the list of participants. Hosius ostensibly supported Alexander of Alexandria against Arius. After the Council, Hosius returned to his diocese in Spain. - Hosius of Corduba
So why was the term homoousios used in the Nicene Creed? It quite simple: The dogma of the Trinity was at stake.
(Gr. homoousion - from homos, same, and ousia, essence; Latin consubstantialem, of one essence or substance), the word used by the Council of Nicaea (325) to express the Divinity of Christ. Arius had taught that the Son, being, in the language of Philo, the Intermediator between God and the world, was not eternal, and therefore not of the Divine substance, but a creature brought forth by the free will of God. Homoousion was indeed used by philosophical writers to signify "of the same or similar substance"; but as the unity of the Divine nature wasn't questioned, the word carried the fuller meaning: "of one and the same substance". However, not only is homos ambiguous; the word ousia itself was often taken as equivalent to hypostasis (person), as apparently is the case in the anathema attached to the Nicene Symbol. And therefore the affirmation of the identity of nature might be taken in the heretical sense of the Sabellians, who denied the distinction of person. It was only after many years of controversy that the two words acquired their distinct meanings, and the orthodox were able to describe the Trinity as one in ousia and three in hypostasis or persona. Previously to the Council of Nicaea, Tertullian had already used the Latin equivalent of Homoousion, conceding to Praxeas the Sabellian that the Father and the Son were unius substantiae, of one substance, but adding duarum personarum, of two persons (Adv. Prax., xiii). And Dionysius of Alexandria used the actual word in a letter to Dionysius of Rome (Athan., "De dec. Syn. Nic.", xxv, 26) and again in his letter to Paul of Samosata. On the other hand, Origen, who is, however, inconsistent in his vocabulary, expressed the anti-Sabellian sense of Dionysius of Alexandria by calling the Son "Heteroousion". The question was brought into discussion by the Council of Antioch (264-272); and the Fathers seem to have rejected Homoousion, even going so far as to propose the phrase heteras ousias, that is, Heteroousion, "of other or different ousia". Athanasius and Basil give as the reason for this rejection of Homoousion the fact that the Sabellian Paul of Samosata took it to mean "of the same of similar substance". But Hilary says that Paul himself admitted it in the Sabellian sense "of the same substance or person", and thus compelled the council to allow him the prescriptive right to the expression. Now, if we may take Hilary's explanation, it is obvious that when, half a century afterwards, Arius denied the Son to be of the Divine ousia or substance, the situation was exactly reversed. Homoousion directly contradicted the heretic. In the conflicts which ensued, the extreme Arians persisted in the Heteroousion Symbol. But the Semi-Arians were more moderate, and consequently more plausible, in their Homoiousion (of like substance). When one considers how the four creeds formulated at Antioch (341) by the Semi-Arians approached the Nicene Creed as nearly as possible without the actual word Homoousion, there may be a temptation to think that the question was one of words only; and the Councils of Rimini and Seleucia (359) may seem to have been well advised in their conciliatory formula "that the Son was like the Father in all things, according to the Holy Writ". But this very formula was forced from the Fathers by the Emperor Constantius; and the force and fraud which the Semi-Arians used throughout the greater part of the fourth century, are proof sufficient that the dispute was not merely verbal. The dogma of the Trinity was at stake, and Homoousion proved itself to be in the words of Epiphanius "the bond of faith", or, according to the expression of Marius Victorinus, "the rampart and wall of orthodoxy."
It is also true that the Council of Ephesus forbids the writing of new creeds, but it does not forbid explaining the decrees in a clearer manner. This is the reason why homoousion was eventually dropped.
Nicaea dealt primarily with the Arian controversy. And Constantine was torn between the Arian and Trinitarian beliefs. Thus he was obviously a believer, even though a catechumen at that time. Athanasius, wrote that it was "the Fathers" who decided on the word. Many of these bishops still remembered the Roman persecutions and would naturally not be overly influenced simply by Constantine. The proof of this is that the Champion of the doctrine of the Trinity, Athanasius was eventually exiled by the Emperor Constantine who was influenced by the Arians.
Bishop (or Patriarch, the highest ecclesial rank in the Centre of the Church, in Alexandria) Alexander ordained Athanasius a deacon in 319. In 325, Athanasius served as Alexander's secretary at the First Council of Nicaea. Already a recognized theologian and ascetic, he was the obvious choice to replace his ageing mentor Alexander as the Patriarch of Alexandria, despite the opposition of the followers of Arius and Meletius of Lycopolis.
At length, in the Council of Nicaea, the term "consubstantial" (homoousion) was adopted, and a formulary of faith embodying it was drawn up by Hosius of Córdoba. From this time to the end of the Arian controversies, the word "consubstantial" continued to be the test of orthodoxy. The formulary of faith drawn up by Hosius is known as the Nicene Creed. However, "he was not the originator of the famous 'homoousion' (ACC of homoousios). The term had been proposed in a non-obvious and illegitimate sense by Paul of Samosata to the Fathers at Antioch, and had been rejected by them as savouring of materialistic conceptions of the Godhead." - Athanasius