Good question. The history of this issue is that "their" and "them" have come to be used as more space-efficient and practical alternatives to, "his or her" and "s/he", respectively. For a long time there was resistance within the professional writing community to using "their" because, of course, its plurality is wrong, as you noticed. :) But in time that objection was overcome, and now it's standard practice.
and this few sentences -> and these few sentences