The minimum range required by C is actually -32767 through 32767, because it has to cater for two's complement, ones' complement and sign/magnitude encoding for negative numbers, all of which the C standard allows. See Annex E, Implementation limits of C11 (and C99) for details on the minimum ranges for data types.
Your question pertains only to the two's complement variant and the reason for that is simple. With 16 bits, you can represent 216 (or 65,536) different values and zero has to be one of those. Hence there are an odd number of values left, of which the majority (by one) are negative values:
1 thru 32767 = 37267 values
0 = 1 value
-1 thru -32768 = 32768 values
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65536 values
Both ones' complement and sign-magnitude encoding allow for a negative-zero value (as well as positive-zero), meaning that one less bit pattern is available for the non-zero numbers, hence the reduced minimum range you find in the standard.
1 thru 32767 = 37267 values
0 = 1 value
-0 = 1 value
-1 thru -32767 = 32767 values
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65536 values
Two's complement is actually a nifty encoding scheme because positive and negative numbers can be added together with the same simple hardware. Other encoding schemes tend to require more elaborate hardware to do the same task.
For a fuller explanation on how two's complement works, see the wikipedia page.
