Step 1: Recall the aromatic test. A ring is aromatic if it is cyclic, flat, fully conjugated and carries $(4n+2)$ pi electrons. If instead it has $4n$ pi electrons, it is antiaromatic and lacks aromatic character.
Step 2: How to read the figures. Since this is a figure-based question, look at each ring drawn and count its pi electrons (each double bond gives $2$, a lone pair in a $p$ orbital gives $2$, an empty $p$ orbital gives $0$).
Step 3: The aromatic species. Rings such as the cyclopentadienyl anion have $6$ pi electrons ($4n+2$ with $n=1$), so they are aromatic. The benzene-type ring with $6$ pi electrons is also aromatic.
Step 4: Spot the odd one. The ring that has $4$ pi electrons (for example a cyclobutadiene-type or cyclopentadienyl cation-type ring) fits $4n$ with $n=1$, so it is antiaromatic.
Step 5: Apply the conclusion. The species with $4$ pi electrons is the one that lacks aromatic properties, which is Fig C.
Step 6: State the answer. So the non-aromatic choice is Fig C. \[ \boxed{\text{Fig C}} \]
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