I answered by asking a question of my own. "Why do property lines exist?" I asked him. "Why do we make sure that we mark the beginning and ending boundaries of our lands? The answer (as I'm sure most people know) is so there is no confusion or encroachment by others. Property lines define the beginning and the end of my land. As a landowner, it is important to know where that land starts and stops. I shouldn't assume land that isn't mine as much as another shouldn't assume to own land that I paid for. I also have to care for my land; it should be both nurtured and protected.
This idea of defining boundaries is also important when discussing religious beliefs. For example, not every religion could be considered theistic. Zen Buddhism is a faith that really doesn't believe in a God as such-- it is an atheistic faith. Other religions hold to differing beliefs about the nature of God, and still more about who Jesus is.
One of the ways Christianity has set up its defining lines is by the historic creeds of the church. The early church fathers knew that this would happen as they were warned by Paul who said that others may come and spread a gospel contrary to the true one. The apostle John also warned the Christians that there existed many pseudo-Christs (e.g. anti-Christs) even during his time. So it shouldn't be a surprise that the church when confronted with a heretical belief would work to make sure Christianity was properly defined. The Nicene Creed was created to be such a boundary point. It is a measuring line to tell what beliefs are necessary for one to be considered a Christian.
The Nicene Creed affirms that God is a single being made up of three persons, it affirms that Jesus was fully God and fully man, it upholds the virgin birth of Christ, and the atoning work of the crucifixion. But the Latter-Day Saints officially reject the Nicene Creed. Each of these doctrines, which are considered essential to the makeup of Christianity, is specifically contradicted in Mormon theology. God is not a single being, but three beings. Joseph Smith considered Jesus a normal man who was just exalted in the same way that every Mormon can be exalted. In Doctrine and Covenants he writes, "The difference between Jesus and other offspring of Elohim is one of degree not of kind." He also taught that Jesus was conceived naturally, from God the Father having physical relations with Mary.
So, in no essential category can a Mormon who holds to the doctrines of the Mormon church also claim to be a Christian without completely destroying the very definition of Christianity itself. This should not be surprise, given that Joseph Smith in his first vision has God labeled these very creeds as "abominations." Therefore, Mormonism by its own admission stands counter to the very beliefs that define what a Christian is.
This is a question that I think has confused many Mormons. They certainly see themselves as a Christian denomination and are quite confused at the hard lines being drawn by those who follow the historic Christian faith. Hopefully, my response to this student will bring a bit more clarity to others as well.
References Galatians 1:6-9
 1 John 2:18
 Doctrine and Covenants 93:21
 The History of Joseph Smith 1:19. See https://www.lds.org/scriptures/pgp/js-h/1?lang=eng