Christians believe that Jesus Christ was fully God and fully man. Three main conceptual problems challenge the logical possibility that Jesus is God incarnate (God and man): 1...Jesus could not be created (human) and, at the same time, NOT created (God). 2...He could not be omnicsient (God) yet have limited knowledge (human). 3...Even if it is possible that Jesus is omniscient, Jesus does not appear to be omniscient. The issue of Christ as God-man is mentioned in Philippians 2:5-11. Paul says that before the incarnation Jesus existed "en morphe theou" (in the form of God). He also says that Jesus emptied himself "en homoiomati anthropon genomenos" (by being made in the likenss of men). this means Christ was human, and didnt just appear to be human. Paul says Christ "emptied himself" which some might interpret as him giving up his divine nature, but this probably means he gave up the privilege of exercising his divine powers WITHOUT giving up his position as God.Thomas T. Morris wrote The Logic of God Incarnate to defend the doctrine's coherence. in it he makes three basic distinctions of th mind and will of Christ. One distinction is between the individual essence ("the whole set of properties individually necessary and jointly sufficient for being numerically identical with that individual") and kind-essence ("a shareable set of properties individually necessary and jointly sufficient for membership in that kind"). No one can have more than on individual essence (God and man for example), butthe can have more than one kind-essence. Jesus Christ is a combination of a fully divine kind-essence and a fully human kind essence. Another important idea when dealing with Christ as a God-man is that of common and essential properties. Common human properties are properties that most humans have, while essential human properties are properties that one MUST have to be human. Christ as all the essential properties, but not all of the common properties.While the idea of Jesus being omniscient but with limited knowledge seems like a contradiction. Morris attempts to explain this using his theory of two minds. He says Christ had a divine mind and a human mind. The divine mind was omnicient and the non-omniscient human mind was only allowed to tap into the divine mind when the divine mind granted it access. Psychologists today say the human mind is not always consciously aware of what it knows. So it was with Christ's human mind. All these above mentioned arguments present a case that says it is POSSIBLE that Christ was in fact God and man, which is the first step to proving it is PROBABLE.

"You can't trust the gospels. They're unreliable."

Many skeptics will claim that the records of Jesus' life found in the Bible are mistaken or falsified. They say that early Christians made up many of the facts of Christ's life and ministry, and that the entirety of the gospels is unreliable. But there is no proof that Matthew, Mark, Luke, and John are doctored in any way.
To display the Gospels' validity, it must first be assumed that they aren't holy books, but merely historical records.Skeptics need to treat them just as they would treat any other normal book of history, therefore eliminating any bias against Christianity. Many skeptics accept the authenticity of other historical documents, such as Gallic Wars, Jewish Wars, Annals of Imperial Rome, and uncanonized gospels, even though the were more likely to be falsified.
If the Gospels have indeed been altered, then it can be assumed that any and every other historical record has been as well. Over 5,000 manuscripts of the New Testament have been discovered, compared to other historical documents supported by only a handful. It is extremely prejudiced to say that the Gospels have been manipulated but these documents with minimal proof haven't.
Just like any other historical book, the Gospels should be considered correct until they are proven otherwise. Skeptics have no reason to question their authenticity.