The idea of Humanism (that people are rational) became widespread as part of the Renaissance. The idea came out of the study of humanities (history, language, poetry, etc…) of the classical world. People who studied humanities had a much broader education and so were more rounded and had a strong moral ethic. There was an emphasis on the individual being part of their community and civic duty.
Humanism was a break away from more traditional learning which had been dominated by the clergy. This led to a more flexible approach to thinking about things that was not rooted on past traditions. Humanism was a direct development of urban living where the church’s control was diminished because of the development of civic society and commerce. It was also an age when science started to become more influential on how people thought (for example empiricism and critical thinking).
So to say that Humanism was a movement away from Christianity is probably a too simplistic view of things. Humanism was more a realisation that Christianity provided one way of looking at things but Humanism showed that there were also many other ways just a useful and valid. It is probably more accurate to say that Humanism provided an alternative to Christian thought. I do not think that any Renaissance Humanist would have called themselves Atheist and it must be remembered that Classical Humanist writings had proved strong influences on many Christian thinkers of the past (for example, St Thomas Aquinas).