One reason for including certain material in the education of "all mathematicians" ... my example is complex analysis. You may end up teaching at a small college, where you teach all undergraduate math courses. Including complex analysis, since engineering and physics want their students learn it. And it is desirable that the instructor know more than just what is in the textbook.
Many times I have heard complaints of this kind... "My research is in graph theory so I will never need to know complex analysis, why do I have to waste time learning it?"