Humanism doesn't assert that animals don't have value, but simply that humans have value. More importantly it claims that humans must be the solution to human problems, as opposed to deities. Considering value in this definition is a broad and subjective philosophical word, it can certainly be compatible with an scientific understanding. Also it's not really pride, although pride in moderation is a good thing. We should be proud of ourselves and of humanity for many things, and disappointed for other things. The fact that we evolved doesn't mean we shouldn't value human life.