It’s from experience. This meme was exactly how I felt before I realized I’m trans. You’re never going to come to that realization yourself if you’re never exposed to the possibility that that’s an option. If someone is confident in their gender identity, they shouldn’t have any problem being called an egg.
Are you going to say gaydar is offensive? We just have a knack for identifying our own.
As you said, most people hate pedophiles. So by constantly labeling trans people as pedophiles, transphobes are trying to get most people to hate us.