For me that moment of realization came about three years ago, on an entirely different forum.
I came into a discussion (on a topic similar to this) between a female friend of mine and another guy a few hours after it started. Every post of his had me nodding: I probably would have said just the same thing if he hadn't beaten me to it. So it was frustrating and confusing to see my friend getting increasingly hurt and angry as they went: why couldn't she see how much this guy was making sense?
I was pretty intensely annoyed with her by that point. I decided that if I was going to be able to get through to her about why she was being unreasonable and this other guy was right, I'd have to dig through some of the links that she'd shared so I could make a convincing case that her position was unfair.
I read the articles she'd linked to, and I still couldn't figure out why she'd been so upset. Confused, I read them again. Then I read some of their links, and theirs, and began hunting for more. What had begun as a determined mission to convince my friend that she was blowing things way out of proportion gradually turned into a dawning horrified realization that I had been solidly and unthinkingly on the wrong side of this whole range of issues for years (despite thinking that I was very committed to gender equality).
Only those few hours of delay before I'd seen the original conversation had saved me from being the one saying totally insensitive and hurtful things to my friend, and I can still think of times in years past when I did say things that make me cringe today. Ever since, I've taken it as a sort of penance to try and share what little of this stuff I've started to understand whenever I see people talking about these issues the way I used to. I hope that it occasionally plants a seed of understanding for someone, even if it doesn't take hold right away.