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The main theme of the book is that males tend to be stronger at "systemizing", that is understanding systems, while females tend to be stronger at "emphasizing", which involves understanding human emotions.
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Here is my big hurdle in understanding all this: How is an aptitude for "systemizing" fundamentally any different than an aptitude for "empathizing"? I just can't figure out how human beings, including all their thoughts and emotions and everything else, aren't systems themselves.

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This doesn't seem very complicated. Historically, males have been the warriors, hunters, builders, etc. and have a certain aptitude for understanding systems relevant to these pursuits. Females have raised children and are better adapted for nurturing and responding to human needs and emotions (empathizing) since that is basically the essence of child-raising. You are trying to make this too complicated with your "but aren't humans systems?" line, and I doubt you are really struggling with this concept (maybe trying to show your deeper understanding of systems thinking?).