I think selection for intelligence was a feedback loop. I think you're interpreting my idea as circular, and I disagree.
Here's what I think was part of what lead to the development of large brains (and general intelligence). Keep in mind that biology and psychology are not my fields.
Intelligence was inherently advantageous for humans because they allowed us to operate better in different environments. That's where natural selection took effect.
Human tribes were and are (like most populations of social species) characterized by hierarchies, particularly among males in the species. Females tended to choose (and still tend to choose, as far as we can tell) males higher up in social hierarchies when all else is equal (just like most social species, even favoring position in a hierarchy more highly than most other traits). If a tribe has many different possible kinds of hierarchies for males (e.g. they inhabit many different kinds of environments), then one trait that enables a male to do well across many hierarchies is general intelligence. When females select males as high up the hierarchy as possible (in general), they are in effect sexually selecting for intelligence.
I think something similar likely happened with males selecting females with higher intelligence, but it was likely more subtle of a process than I can grasp, since males tend to mate far less selectively than females among humans (and most other animal species), which complicates it quite a bit for me.
Also, just because a choice is unconscious does not mean it is illogical. Many unconscious human choices are quite logical and make a lot of sense, but are not well suited to our current environment.