noun. An illogical reasoner. Opposite of a logician.

The baffled illogician, persecuted in one position, flees into another.
Obiter dicta, Augustine Birrell (1884)

Also known as: a politician.

The fanciful title of illogician is not reserved for those in politics and government, this moniker can be bestowed upon a cornucopian amount of other individuals: Bosses, teachers, lawyers, bankers, parents, children, anyone in the DMV, drunks (but they at least offer enterainment), the list continues. Feel free to contribute others in the comments.

My mother is an excellent example of an illogician:

I can’t hear you, I don’t have my glasses on.
Mi madre (2006?)

Need I say more?