Mainstream Christian groups limit the term 'Christian' to those who believe Jesus is the Christ and agree with them about what that means. The term 'Christian' isn't used for anyone who simply likes Jesus or believes he was special in some way. We can see this because Islam teaches that Jesus was a prophet, but Muslims aren't called 'Christian'! Similarly an atheist who thought Jesus was a good teacher wouldn't be called a Christian. Clearly it's more than just thinking highly of Jesus.
At the barest minimum, the term 'Christian' is used for people who believe that Jesus is the Christ, the Greek word for the Hebrew concept of the Messiah. The Messiah is a character prophesied about in the Old Testament, though there is much debate in and outside of Christianity as to what exactly it means to be the Messiah. Both mainstream Christian and restorationist groups such as the Mormons and Jehovah's Witnesses agree this far; they disagree, and limit how the term is used, because of what they believe the Messiah means.
What you call 'mainstream Christianity' is Trinitarian Christianity: they believe that the Messiah is God himself, who came incarnate to the earth. They call the other groups non-Christian because they believe the Jesus they proclaim actually has a very different identity. To Trinitarians saying that Jesus is a created being, is a 'mode' of God, or that he only became divine at his baptism is just as wrong as saying that God doesn't exist and Jesus was nothing more than a human teacher.
Trinitarian Christians find support for their views in the historical creeds, such as the Apostles' and Nicene creeds. Though there were dissenters at the time those creeds were written, no church today is directly descended from them, and at the times when these non-Trinitarian churches were founded the creeds were accepted by all other Christians.
Lastly, note that sometimes a group likes to reserve the label 'Christian' only for those who hold very similar beliefs to their own. You will find many protestants who will call the Roman Catholic Church a non-Christian organisation. They refuse to call the other side 'Christian' because they believe they have distorted the gospel or replaced it with a completely different gospel.