I don't agree that it is a common phrase but I will give you that. So what is it saying in the context of the post without being completely besides the point?

I mean I think you would agree with me, if I would say that, saying "you aren't a good person if you have to say it" would be off-topic as a response to someone who would say that when they hear that someone wants to feel like they are a good person, they think they are a bad person. I am changing the context to highlight why I think it would be completely besides the point. In that case, I think you would be right to take it literally and accept it as a off-topic response. But if it would be a reaction gif, you probably should ask yourself if it is wise to read it literally as an off-topic response or adapt it a little to fit the topic.

Now back to the real thing, The literal reading is toxic, and e.g. transphobic because it says that coming out makes you not a man. The little adaption that I think would be a valid way to match it in the context, is to change "says" to "says that they want to feel like". Maybe it seems big but I honestly think it is an adaptation required for most reaction gifs or meme templates. But as it is still toxic and transphobic, I am not too interested in arguing whether or not I am wrong to read it like that instead of literally.

Now you are saying that it is a common phrase that says that if you make a big deal out of being something, you aren't that. That sounds like the literal reading of it. So we are back at off-topic toxic, and e.g. transphobic statement. Because guess what being trans and coming out and transitioning seems like making a big deal out of it. I think it is a big deal and they have very right to do so. I hope their experience is pleasant. At this point, it seems like you think they shouldn't and that doing so makes them not a real e.g. man. I don't think you think that but to me, your argument seems to point there. Would you be motivated to tell me how that is not the logical conclusion?