Doesn't the Special Theory of Relativity explain the Michelson–Morley experiment well?

Yes, it does so.

But that does not mean it is right.

The Michelson–Morley experiment was designed to detect the relative motion between the Earth and Aether, the assumed stationary medium of light.

To me, the theory of Aether has two flaws.

First. If everything is moving in the universe, why Aether is stationary?

Second. If the Earth is carrying everyone of us, carrying the thin air, why it refuses to carry Aether?

I read somewhere that Aether can not be moving with the Earth, else some kind of light aberration can not be explained, but it is mentioned without any details. As an outsider, I have no idea what that is about. If anyone has a detailed explanation, could you please let me know? Your help is really appreciated.