It's not enough to simply like Jesus or believe he was special in some way, because Islam teaches that Jesus was a prophet but no one would ever call Moslems Christian! Similarly an atheist who thought Jesus was a good teacher wouldn't be called a Christian. Clearly it's more than any of that.
If you want to be called a Christian the starting point must be that you believe Jesus is the Christ, the Messiah. You must believe Jesus is the long foretold anointed king and saviour of Israel. But that's not a full explanation as it would still include many who those mainstream Christians want to exclude.
As well as believing Jesus is the Messiah, such groups believe it is very important that you have the correct understanding of the Messiah. 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, 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. In such cases it really means that your beliefs are correct on all the major points, which is very subjective.