There are a few canards we should dispense with in discussing this issue.
First, it is dubious to argue that because the word does not appear in the New Testament that "trinity" is not a biblical concept. The word "omnipotent" doesn't appear either, but it's clear from what the bible DOES say that the God described in scripture is omnipotent. What holders of the trinity doctrine affirm is that the NT contains expressions and intuitions which ENTAIL the trinity.
Second, and this is related to the first point, the doctrine of the trinity didn't just all of a sudden appear out of nowhere in the context of fourth and fifth century debates; nor was the discussion an ivory tower affair among high-falutin' philosophers. This was (and is) a bread and butter theological issue with serious implications for ecclesiology (theology of the church), missiology (theology of the church's task), and soteriology (theology of salvation). It is simply a matter of historical fact that differing views of God lead to much different understandings of everything else. I leave for homework checking that out.
Third, the doctrine of the trinity, in its nicene formulations and following did in fact use technical language and even had to invent or reapply existing terminology in order to make the formulation. (I have in mind here the substance/person distinction.) As a result of this, people have accused the church of lapsing into paganism or incoherence. Not so. Understandably, the intuitions I referred to in my first point provoked questions from the church and from those the church sought to reach. To answer these questions required a certain reinvention of language. Those basic intuitions required some high-falutin' philosophical work by people with more brains than most of us can ever hope to presume to have, yet the trinity is accessible to laypersons. If it weren't, there wouldn't have been any point in elaborating the trinity. How could anyone hope to respond to a message that was utterly incomprehensible?
That said, misunderstanding is possible. Some of this is a matter of figuring out the concept. Admittedly, it's not immediately straightforward, but it doesn't take a Ph.D. to get it. But some of it is really just churlishness, a sort of determination not to understand it. This latter attitude, although intellectually deplorable, is understandable as a form of defense. "I don't have to believe this stuff because it's completely stupid or beyond my ken or whatever." This attitude is especially present in those who hold that the bible is somehow (or somewhat) authoritative but do not identify with the historical church. So I suggest that this is more of a political issue than anything else. To admit that the trinity is the best interpretation of scripture would be to challenge their group's break with the historical church (among other things).
Lastly, debates over whether the doctrine is biblical are usually doomed for reasons related to issues I rasied in the previous paragraph. So it can be quite exasperating discussing this topic. But perhaps they can bear some fruit if both sides (assuming there's only two -- yeah, right!) are willing to see where the other side has a point. This is possible without having to agree with the other's case. And I find that most discussions of the trinity devolve rapidly to name-calling because both sides see this as a no-holds-barred death match. That is, we forget that, however else we might describe God, he is love, and we who claim to be articulating a faithful vision of this god undercut ourselves in the way we approach these discussions. So there needs to be a place for genuine respect and love for the other in these discussions, and I'm sorry that I haven't been the best example of that in the past.
Anyway, lost focus a bit as this post got on. Apologies.
