Personally, I don't think that taking HRT will actually make a man understand women any better, so perhaps my response to GP should have been that.
Edit: fix op/gp monikers
In my experience, the best way to understand how women experience the world is just as you said: spend time with them, talk to them, and - most importantly - listen to them. I think many men could benefit from having more female friends (and I mean truly friends, not secretly trying to get in their pants).
I've learned so much about how differently women experience the world just from befriending many women over the years. It's really opened my eyes to how differently women might experience the same situation. It's amazing how different society treats women and it can be totally invisible to men unless you're willing to look for it. I think it's made me a better husband and father as well.