Comparing Wings

[Tanarii]

This isn't quite right, per se. All spells and magic items are considered magical, and are blocked inside an anti-magic field. Also, yuan-ti, satyrs, or character's wearing a robe of the archmage have advantage on saving throws versus those magical effects. There are also some magical effects that aren't spells, such as a basilisk's gaze; they would also have advantage on saves against the gaze, and an anti-magic field would block it. A dragon's breath is not considered magical, so you wouldn't get advantage to your save, and anti-magic does nothing.

This is kind of what you're saying, but the distinction can be important. Dragon breath isn't magical, so effects that stop or protect against magic don't do anything. It could be accurate to say that dragon's breath is a supernatural ability, however, which isn't that different from saying it's "magic". But there are also things like the basilisk's gaze, which is magical, and thus can be stopped by anti-magic.

Dragons breath is magical. As is Ki, Channel Divinity, etc. That's the point.

From the Sage Advice Compendium:
You might be thinking, “Dragons seem pretty magical to me.” And yes, they are extraordinary! Their description even says they’re magical. But our game makes a distinction between two types of magic:
• the background magic that is part of the D&D multiverse’s physics and the physiology of many D&D creatures
• the concentrated magical energy that is contained in a magic item or channeled to create a spell or other focused magical effect