Acidity order checking for α-furoic acid and acetic acid
The conjugate base of 2-furoic acid is aromatic, but so is the acid. 
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The aromaticity does not contribute to the stability of the conjugate base because the negative charge from the carboxylate anion cannot delocalize into the ring. The major resonance contributors for the carboxylate anion are:



However, because of the oxygen atom, furan is an electron-rich arene, and one position that has higher than expected electron density is the 2-position:



Furan is therefor electron-donating, and electron-donating groups destabilize anions. Consider the following resonance contributor of 2-furoic acid and the close proximity of the formal negative charges: