Diamonds are also not rocks

Ah, this is actually more illuminating than I'm sure you've intended. Diamonds are rocks. They're metamorphic rocks. However, some people might consider them rocks while others do not. Rocks are an aggregate of inorganic materials, and certainly one wouldn't consider a diamond to be organic. But then again, chemically speaking, organic compounds are usually carbon-containing, and inorganics usually carbon-excluding. So wow, I guess the idea that all rocks are rocks is a bit misleading.

Then again, I doubt very much that I need to describe to you the intricacies and inadequacies of categorizing in a way that is both broad and rigid. You've given yourself away by stating, seemingly unironically, that "all females are Chad chasers."