Why did our fathers in the faith invent such theological terms?
The term “Trinity” was developed out of necessity after three centuries of theological controversy concerning the deity of Jesus Christ.
Several theological terms were defined and debated during this time including: Essence, Substance, Subsistence, Hypostasis, Person, Trinity, Homoousion, Emperichoresis, etc.
One of the favorite objections of the arch-heretics was that such terms did not come directly from scripture and therefore had no authority. For example:
Arius wrote, “Why is the word, of which neither the prophets nor the apostles make mention, added to the apostolic faith?” 
Curcellaeus agreed that it was better “to return to the simplicity of the sacred writings, and reject from them all words invented by men, or at least compel no one hereafter to swear by them.” 
The orthodox have always agreed that extra-biblical terms ought not to be introduced into the church rashly and unnecessarily, but this is not the central question.
The chief question is this: Is it lawful on occasion to employ extra-biblical terminology for the sake of explaining scriptural doctrines more plainly and for refuting heretical doctrines more completely?
The orthodox have always answered this question in the affirmative and we shall allow them to explain why:
Gregory Nazianzus – “We must not contend spitefully about terms as long as the syllables lead to the same opinion.” 
Augustine – “We confess that these terms were produced by the necessity of speaking, since there would be need of a copious disputation against the snares and errors of heretics.” 
Augustine – Commenting on 1 Tim. 6:20, “The apostle does not say the newness of words must be avoided, but [he adds] profane; for there are doctrines of religion agreeing with the newness of words… the things themselves called by new names were before their names.”
Thomas Aquinas – “The necessity of disputing with heretics compelled them to invent new terms expressing the ancient faith.” 
1. Vigilli Tapsensis Contra Arianos 1.10 [PL 62.131]
2. “Prima Dissertatio Theologica: De Vocibis Trinitas,” Section 11, Opera Theologica , p.816
3. Oration 39, “On the Holy Lights” [NPNF2, 7:355; PG 36.346]
4. Augustine, The Trinity 7.4 [FC 45:233; PL 42.941]
5. “Tractate 97,” On the Gospel of John [NPNF1, 7:376-76; PL 35.1879]
6. Summa Theologica, I, Q. 29, Art. 3, p. 158
For a fuller treatment of this question, please consult Francis Turretin’s Institues of Elenctic Theology, Third Topic, Q. 23.