Take, for example, the idea that Jesus is "the Son of God." What do Christians mean by this? Did the Father have sex with a woman to create him? Well, no. Christians tend to see that as highly blasphemous. They maintain that Mary was impregnated by some supernatural means that's never actually explained, and was a virgin when she gave birth to Jesus. Okaaay... well, surely the Father created Jesus in some sense, right? Well, no. In fact, Christians are adamant that he was never created. According to the Nicene Creed, the Son was "begotten, not made" and has always existed alongside the Father.
It's not even clear that it makes sense to talk about the Son as inherently male. Sure, the Bible has Jesus temporarily incarnated as a man, but in general, God is supposed to be a perfect spiritual being who transcends such earthly concepts as gender. Or do Christians think Jesus is up in heaven right now as an actual male, sitting at the right hand of the Father complete with an immaterial, spiritual penis?
All right, fine. If Jesus wasn't the product of sex, and has always existed, and isn't male in any meaningful sense, maybe it's just a metaphor of some sort. Calling Jesus "the Son" could mean that he's in some way inferior or subordinate to the Father. Well, no. One might think so after looking at certain biblical passages, but according to the widely accepted Athanasian Creed, the three persons of the trinity are "co-equal" in power and authority. Jesus is supposed to be fully God in every respect. In what sense, then, can Jesus be considered the Son of God? That's for believers to determine.
There are dozens of these little sayings and points of doctrine that are accepted without any reflection from most Christians. What does it mean to say that Jesus is "the Word of God made flesh"? What does it mean for God to be "outside of time"? In what sense can Jesus be considered "fully God and fully human"? How can God be viewed as a single being when he exists in three distinct "persons"? If Jesus "paid our ransom" to set man free from sin, to whom was that ransom owed?
I doubt that it would even be possible to coherently answer all these questions. But even if it is, there's a deeper problem here: the vast majority of Christians don't even attempt to find those answers. In most cases, it doesn't even occur to them. They read or hear that Jesus is the Word, or that God exists outside of time, and they never think to ask what it might mean. Hundreds of millions of people are satisfied—even enraptured—with a religion held together by buzzwords. They thrive on what Eliezer Yudkowsky has called "mysterious answers to mysterious questions"—that is, non-answers that halt curiosity without furthering our understanding.
That's why the skeptical outlook is so important. In some cases, challenging people on their religious beliefs will only cause offense. But if we can teach people to habitually investigate extraordinary claims, many will apply that principle to their religion and start asking questions all on their own.