Let me tell you why I believe the gospel, rationally speaking.
Let's approach the four canonical Gospels—the only biographies of Jesus believed to be put to writing within a generation of his life (for comparison, picture a book written today about John Lennon)—as if they were any other ancient document that claims to depict historical events. We have to approach them with an innocent-until-proven-guilty mindset. We don't assume that they're 100% true and accurate, but we assume that they're basically accurate unless we find some evidence that points otherwise. We don't discount them just because they claim supernatural causes for events and miraculous happenings. All ancient historical documents do that. If we were to discard every ancient historical document as useless if it talks about the supernatural, or if we were to say that a book tells us nothing if there's anything inaccurate in it—guilty until proven innocent—then we would have no knowledge of ancient history at all. Zero. So just like we do to Tacitus, Livy, Plutarch, Herodotus, and the like, we assume that the canonical Gospels are basically true unless we find something we know can't be right.
Well it happens that all four Gospels claim that Jesus died by crucifixion and came back to life "on the third day" (if Friday, the day of his death, is the first day, which is how they counted things in that culture), and that after that he went directly to heaven instead of dying again. That's the kind of crazy talk that would lead us to discount those portions of each of these books. But the problem is that we have four roughly contemporaneous written witnesses to the life of Jesus, and all four contain this. And each of these written witnesses recounts the stories of multiple witnesses who claimed to see this—not all the same ones either—and even gives their names, so if you read one of these Gospels when it was first written you could conceivably track down the witnesses and ask them yourself. We don't have any account of the life of Jesus so close to when it happened that does not attest to his resurrection in multiple ways. Even though it is ridiculous, that makes for a pretty strong claim.
Even more perplexing, try as we might we can't find any convincing alternative explanation for this. One might claim that Jesus didn't really die. Given the physical abuse he endured, that's astonishing enough, much less how he rolled away a huge boulder from the mouth of his tomb, singlehandedly overcame a squad of armed Roman soldiers, and convinced the people who saw him that he was immortal rather than in serious need of medical attention. Another possibility is that the disciples stole the body and made up the story—indeed, according to Matthew this is the story that the chief priests encouraged. But if so, why were they so willing to risk their lives—and almost to a man spend them horrifically—for something that they knew wasn't true? I can imagine what a cult leader might gain from duping his followers, but where do savage beatings, crucifixion, and being fed to the lions fit into this? Maybe Jesus' followers—all these different recorded witnesses—somehow experienced some simultaneous mass delusion. Despite the glaring question of how this could have happened, there's the fact that the Jewish Council would still then have been in possession of Jesus' body and could have produced it and squashed the rumor of resurrection as hysterical right there and then. Sure, some people might still have believed that Jesus was alive (and that Elvis is still living), but it never would have caught on like it did. And it doesn't answer the question of why Paul, who claimed to see the risen Jesus long after everybody else, endured such suffering as well.
So if there is uniform testimony from multiple witnesses that Jesus came back to life after dying and that he went to heaven bodily without dying again, and if there is no plausible alternative explanation, then I have to believe that Jesus' resurrection and ascension actually happened.
Now, if this man Jesus really was stronger than death that way, that makes him totally unique among all people who have ever lived. I don't know of a single other person who died, came back to life, and then didn't die again after that. And I find that extremely interesting, because I would really rather not die. That's probably more important to me than anything else when it comes right down to it. So if I'm looking for advice on how not to die like everyone else, or at least not die permanently, Jesus really seems to be the only one to go to, because he is the only one with a better than 0% success rate. And I had better take what he says really seriously; who am I to argue with him when he's the one who is stronger than death and I'm not?
When I read what Jesus said I start finding all kinds of amazing claims. There is a God who made everything. Jesus is his Son in a unique way. In fact, Jesus existed before God made everything else. He has the authority to do what only a Righteous Creator God can do, everything from stop storms to forgive sins. And he lays down the law about what is right and wrong; he says that everyone but himself violates that law and thereby sins. In addition, he also repeatedly claims that rejecting those sinful ways and trusting Jesus himself is the key to life for everyone else, from being healed to having your sins let go by God to living forever. If I want those benefits, I had better do what he says. So I repent of my sins and put my trust in Jesus to save me.
Jesus also teaches lots of other things about the world and how it works and why things happen the way they do that I haven't mentioned here. But one of those things that is particularly interesting is how he regards the Hebrew Bible or Tanach, which Christians call the Old Testament (which is another story). He repeatedly talks about it as if it is the word of God—that is, as if the people who wrote those works were either taking dictation from God, being imperceptibly moved to write what they wrote by God, or something in between (depending on the book), so that all the books that make up the Hebrew Bible are God's written communication to humanity and intrinsically true. We don't have any evidence that he regarded the Hebrew Bible as anything but the word of God; the testimony is uniform. So once again, if I really want to overcome death, and I take Jesus' advice seriously in order to do that, then I have to conclude that the Hebrew Bible is God's true word too.
By now I have to grapple with the fact that I'm getting this knowledge from these canonical Gospels that I've considered to be basically accurate without quibbling about various fanciful details. But since I have the infallible standard of truth that Jesus has, the Hebrew Bible/Old Testament, it's worthwhile for me to compare the Gospels to those documents. I find that repeatedly the Gospels reach back to Old Testament texts, themes, and concepts to validate their message. Even when there is some shift, something that I wouldn't expect signalling a new direction, there is a constant appeal to the Old Testament for justification. Jesus himself does this, and the Gospel writers do too. And in fact when I look at the other writings that make up the New Testament, I find the same pattern. Again and again the writers write in such a way that demands Old Testament corroboration for their claims. "As it is written" shows up everywhere. I also note that these books are either written by people who saw Jesus in his resurrected state, most of whom spent serious face-time with Jesus on earth (2 Pet. 1:16-18; 1 John 1:1-3) or were the intimate associates of those who had. I'm beginning to wonder if God has inspired the New Testament writings the same way he did the Old Testament ones. I find that the ancient church believed exactly that, so I have a choice about whether to take their word for it or not. And without going into too much more detail, I do.
I do not believe that the claims that Jesus Christ is the risen Son of God and that the Bible is the reliable word of God can be proven beyond any doubt. But I do believe that these claims and their corollaries can be proven beyond a reasonable doubt. Lots of people have lots of objections to them for lots of reasons. But I've never heard an objection based on reason and logic that doesn't at some point collapse on itself.
That's why I believe the gospel, rationally speaking. Why do you believe—or not?