I can sympathize with those who find Christianity impossible to believe. Even aside from the rampant hypocrisy one can find in nearly any church, there are philosophical problems like the existence of evil that many are unable to reconcile with the idea of a perfect and loving God. Not that anyone has a truly satisfactory explanation for the existence of evil, but whenever a church or denomination claims to have all the answers it understandably raises a lot of skepticism.
Not all stumbling blocks are equally troublesome, however. For my own part, I've never had a problem with the idea that God could simultaneously be three distinct persons yet one being, though I know that concept has caused some to reject the faith. To the contrary, I find it far more illogical to think that a God capable of creating the universe we experience around us could be fully understandable in human terms, as such individuals seem to require.
I do understand the skepticism that many people feel when a paradox is presented to them. Adherents of the "God said it, I believe it, that settles it" school of mindless faith have used their catchphrase to justify all manner of abusive and destructive behavior, and in the process have done more to discredit the Christian faith than any external enemy could ever have hoped to accomplish.
Furthermore, when we attempt to wrap our minds around things that are beyond our comprehension, it can become difficult to draw and maintain a clear line between paradox and irrationality. By opening the door to the possibility that two apparently contradictory things could both be equally true, we seemingly run the risk of embarking on a slippery slope into a realm where any nonsensical notion must be placed on equal footing with the most well established scientific fact.
But just as there's nothing inevitable (or even probable) about societal acceptance of gay couples leading to acceptance of pedophilia, bestiality and other unmentionable things (except in the lurid imaginations of some fundamentalists), so the acceptance of paradox as a valid way of broadening our ability to describe an indescribable Creator doesn't have to leave us at the mercy of demagogues and madmen.
When two groups of Christians come to irreconcilably opposed conclusions about the nature of God, with strong arguments based on scripture, tradition, reason and experience, it becomes reasonable to argue for the existence of a paradox. Predestination vs. free will, above time vs. within time, perfect goodness vs. the existence of evil - on issues of this sort we can never hope to know for certain what reality beyond our plane of existence really looks like. Yet just as the basic forces of the physical universe (gravity, electromagnetism, strong nuclear and weak nuclear) can only be reconciled if we allow for the existence of multiple dimensions beyond the four that we experience, so we can imagine that theological dilemmas that don't seem to add up now may fit together perfectly when viewed from a five (or ten or twenty six) dimensional perspective.
Regarding the idea of a triune God, consider how any of us would appear to a universe of two-dimensional beings who experienced depth the way we experience time (assuming, for just a moment, that we came up with a way to interact with their reality). A person intersecting their plane of existence would appear as one or more shapes; as we moved through their plane, our shape(s) (and their contents) would change in appearance without any explanation that our two-dimensional neighbors could conceptualize. Our arms, fingers, legs, head and torso might appear at times to be separate entities capable of moving independently and disappearing and reappearing at different times. We could even remove ourselves entirely from their universe and reinsert ourselves at a different point, seemingly without traveling the distance between our previous and new locations.
Consider, then, that a Creator would necessarily be many dimensions beyond us, and suddenly the paradox of the trinity seems like it must be a gross oversimplification of the ultimate reality of such a being. Such speculations are still fair targets for skepticism, since they cannot be empirically proven, but it stands to reason that we should be far more skeptical of any deity or higher power whose descriptions fail to transcend our own four-dimensional limitations.