when you realized that you can now understand the behaviors of both women and men
This really isn't an "aha" moment where you move from not being able to do it to being able to do it.
It's a skill set that will, hopefully, continue to get better and better the more social experience you get.
But for me, this started back in my 30's when I started getting heavily involved in public speaking.
Public speaking increases social confidence, decreases social anxiety and opens up your brain to start noticing things going on all around you.
For most people, it's not really a matter of learning how to do this, rather it's about turning off all the nervous social anxiety driven chatter that allows you to do it naturally.
Reading between the lines, reading the room, understanding the subtext, etc., is a natural part of our evolutionary programming, as we are highly social primates.