Hi Amazing,
I agree with you that the periodic table, as we have it, was deliberately layed out to bring out patterns, and that these simplified groupings are a human construct. The society does tend to exagerate orderliness in nature as evidence for a designer god.
I do want to let other readers realize though that the periodic table as we have it does bring out at least one genuine underlying pattern seen in the natural elements. That elements with identical electron configurations in their outermost shell will behave very similarly/almost identically in their chemical reactions. It was this similarity of chemical behaviour among elements and a seeming periodicity associated with atomic number that gave rise to the idea of setting up a table. (Again its more correct to look at the electron configurations). Elements are placed in the same groups to reflect that underlying natural pattern. But again that doesn't mean a god designed it that way.
I look forward to other thoughts you have on that book. Its less fun to take apart than the earlier book Life How did it Get Here? but there's still ample material to dissect.Later.