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Why in a metal parallel-plate waveguide does TM0 exist and TE0 does not? Or is it...

Why in a metal parallel-plate waveguide does TM0 exist and TE0 does not? Or is it the other way around?

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From mathematical equations, you can easily understand why TE0 not Exist and TM0 exist. For TE0 all components varnished but TM0 has Hx,Ey components exist

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