If your original question is "why is it wrong to reveal people who are transgender," the reason is because there are bigots out there who beat up on trans men and women.
If this was a perfect world, we would all be allowed to be whatever we wanted. But just looking through this thread is evidence enough that you can't say or do something without someone going up your *** about it. This is just a mild comparison too: insults may be just words, but the threats are very real when you see news stories of people getting beat up and even killed just because they are trans, gay, have different religious beliefs, etc.
I'm not going to get involved in the debate you two are having, just laying out the facts of the world we live in. Edit: Because of these facts, this is why it's wrong for someone to "out" trans people. So even if you have the talent to spot them (I'm not going to get into this argument), you're putting someone's life in danger when you out them this way. Hence why it's disrespectful to do so without their consent.
Also gonna add that just because this is the world we live in doesn't mean we shouldn't try to make it better.