Nice post! I wish more people would meta-analyze their own thinking. I do have an issue with one of your tangential presumptions.

"Female" side of the brain? Brains are either fully male or fully female, unless there's some hermaphroditic chimerism going on.

If you said "feminine" I would take less issue, because "feminine" is a cultural (emotional) concept, not objectively real. "Female," in contrast, refers to an objective aspect of reality regarding chromosomal composition and gene expression.

In your emotional experience, women have been less logical, and from there, you have assumed that there is something about women's brains that makes them inherently emotional and illogical. However, your entire post was about how peoples' minds can be trained to go in either direction.

Given that I have met many women who are supremely rational and many men who are severely emotionally irrational, I think the reasonable conclusion is that our social definitions of "masculine" and "feminine" result in women being less likely to be trained to embrace their emotions and men being more likely to be trained to reject their emotions. Perhaps there is a propensity differential as well. That remains to be seen. However, unless you can demonstrate that there is something "female" about irrationality and something "male" about rationality, I'd just stick to calling them the "rational" and "emotional" centers of the brain.