Why do we quantize high frequencies coarsely, shouldn't it be the opposite?
In Huffman coding frequency refers to the number of times a particular sequence of discrete source symbols has appeared in the input. It is not the same concept as frequency in the continuous space such as sound frequency. As such, it has nothing to do with psychoacoustics or the cochlea. 

We use fewer bits for the higher frequency source symbols because frequent source symbols have lower entropy and assigning fewer bits to low entropy symbols gives better compression.