Yes, historically, Christianity's theological contribution was the idea of a god that cares equally for everyone. But western humanism goes beyond that (building upon) in that human life is valuable in itself, regardless of the social, economical and, the big innovation, religious/ideological stand of that particular individual.

All of that is supported by philosophical arguments, giving western humanism a much older foundation than Christianity.

So, succinctly, I would put like this: was Christianity a necessary condition for the development of western humanism? Yes. Was it sufficient? No. Bigger and better ideas were needed to make it what it is today.