Before addressing where anthropology might fit into the overall scheme of things, first let's talk about the sciences vs. humanities "debate." (This "debate" really is the sciences vs. the humanities, the social sciences, and the arts.) As with the nature vs. nurture debate, this is something of a false dichotomy, argued to be a conflict by those only at the extreme ends of both sides, with the truth of the matter being that we are informed by the sciences and the humanities, social sciences, and the arts, as we are made up of both nature and nurture.
Anthropology, considered a social science, basically the study of humans, straddles both sciences and humanities, providing support for both sides of this debate, to the degree that the debate exists. This is particularly true today because there are so many subsets of anthropology. There is the socio-cultural branch of anthropology, which is largely a comparative study of social systems and cultures around the world, falling more on the humanities side. But there are other kinds of anthropology, too, for example, biological or evolutionary anthropology and medical anthropology, both of which fall more on the science side since they deal in "hard" data and phenomena, such as biological and evolutionary characteristics or disease.
No matter what one's field of study is, it is a mistake, in my opinion, to dismiss either side of this debate. There are as many truths to be gleaned from the humanities, social sciences, and the arts as there are to be gleaned from the sciences, and we ignore one or the other at our peril. Our greatest scientists have always understood this, making music, writing novels, and otherwise enriching their own lives and ours in the humanities, social sciences, and arts. Arthur Conan Doyle was a physician, as was Anton Chekhov. Isaac Asimov was a professor of biochemistry. Not a one of these would have thought there was a dichotomy at all!