So far the only concrete advice I've received is from retropunch (regarding the Four Great Books) and mainiac (Regarding the economics section (did not know Capitalism and Freedom was that bad btw, thanks for the heads-up - is Sowell still relevant? I am reading him now, I'd like to know if it is objective. Also, why remove Security Analysis? Redundant, bad or can be better?), everyone else is being too broad in their advice. Suggest actual books (by name!), whether which ones to take out or which ones to add in.
I'd suggest a more recent translation with more emphasis on unambiguity (English is very vague compared to Greek) and clearer language to the modern reader - my favourite is the NIV.
As for the rest, sure. I'm not sure which to replace, but
Ways of Dying captures a lot of the Bantu style and modern culture, and
Things Fall Apart makes heavy use of Igbo oral culture, avoiding the issue you mentioned with the oral traditions.
African Mythology or
African Myths of Origin would provide an overview of the many African mythologies.
Looking over the list again,
The Psychology Book provides an overview of psychology, currently completely unrepresented.
And I agree with pretty much everyone else that literature is highly over-represented on your list. However, if you must have so much, consider adding something that isn't classic literature -
Laura or
A Study in Scarlet or some other classic of crime fiction, and
The Lord of the Rings (or some other archetypal fantasy novel) as a massively influential modernish work of fantasy. The literature section would almost definitely be improved by a literature analysis book, even if you don't think it's as good as all the books currently present.
The Seven Basic Plots would be a start.
Master Basic DIY: Teach Yourself probably doesn't go into quite as much detail as acetech would like, but it covers most simple handyman-type activities - plumbing, wiring, painting, basic construction, and so on.
A Short History of Nearly Everything seems like it might fit in here too, covering such concepts as evolution and geology, as well as a ton of other random stuff.
The Information (James Gleick, in case there are other
The Informations) is a really good book on information theory and the history and theory of communication, but it's pretty niche.
Journey to the Ants is bizarrely specific. Why myrmecology and not melittology? And why myrmecology when it doesn't look like you cover topics like botany?