Why a Trinity?
No Trinity is found in the NT. In the NT Jesus denies again and again that he's god, just as you'd expect of someone raised in Judaism. He says in as many words that the Father is god and is his, Jesus', god, and that he is simply Yahweh's agent doing what Yahweh tells him. If you wish to read those texts, I set them out >
here<. He never once claims to be god.
The best that can be said is that the NT mentions each of Jesus the Son, and Yahweh the Father, and the Holy Ghost (the perennial bronze medalist).
The idea that the three of them make up a single god (often 'godhead' to make the message less bald) is developed in the 4th cent. and arises from the politics of the early church. A major element is the desire to promote Jesus to God status so that he can be worshiped in his own name. The promotion of Christianity to an Empire religion by Constantine in 313 added to this pressure. Up to that time, there had been another as well. In the marketplace rivalry for followers, the people to whom Christianity was likely to appeal included many to whom Judaism might appeal; and Judaism had been exempt from the requirement to attend the ceremonies of the Roman gods while Christianity had not. One of the taunts of Judaism to Christianity in this rivalry was that Christians worshiped more than one god (as the Romans did), while the Jews worshiped the one true god ...
So the Trinity doctrine emerged.
Unfortunately it's incoherent. No matter how you phrase it, you can't have a single god who is three distinct 'persons' each of whom is 100% of god. The problem is acknowledged by the RCC and Anglicans and doubtless others, but (again in order to make the proposition less bald) called a 'mystery'.
So in broad terms, the story of why there's a Trinity goes something like that.
