I'll leave the linguistic battles to those with strong feelings on that issue and just focus on what I think was the original intent of the question...
I felt like there was something not quite right with me for pretty much my entire life, but I could never quite verbalize what felt wrong. I had very little exposure to the idea of transgender people when I was growing up. I was aware that some people had sex-change operations, but the concept never really gelled in my mind as something real. I just knew that I didn't quite fit in anywhere, and that my attempts to blend in with my peers only made things worse. I just could not seem to figure out how to be a proper boy. This continued into adulthood. For about four decades, I was often depressed and rarely happy, because I could not figure out what was wrong with me. I only knew I didn't feel right.
For a time, I had a male roommate. At least, I thought he was a guy when he moved in. I discovered later that he was actually a pre-transition transwoman. Deep inside, something woke up and took notice, but it still took a number of years after that before things actually gelled for me and the idea of being transgender took on some level of reality in the back of my mind.
One morning, when I was about 40, I woke up and just realized that I finally knew what was wrong...I was never really a guy at all, even though I had a male body. It was an a-ha moment that hit me in that gray stage before waking and would not let go even after I was fully awake. I mentally tried thinking of myself as a woman with a female body, and it felt SO GOOD! I felt happy. I felt relaxed for just about the first time in my life. I felt right. I felt GENUINE!
When I went back to thinking of myself as a guy with a male body, it felt downright unpleasant. It felt like a lie. Now, I can't bear to present as male unless I think of it as wearing a mascot uniform (like a blue panda costume or a giant chicken) for my employer. I even joke with my wife about putting on my "giant-chicken suit" before going to work.
That's how I realized. That's how I knew.