Why is cepstrum used in MFCC instead of autocorrelation sequence?
Usually in speech signal processing cepstrum is used to represent low and high frequency components , which are multiplied with each other(in time domain its a slowly varying signal convolved with high frequency signal).  


  What's the reasoning behind using log value?


logarithm is taken to remove the multiplicative effect and convert it to addition of two components. $$\log(a\cdot b) = \log(a) + \log(b)$$


  Why does that make a difference?


Now the two components are in addition form.


  Why isn't the autocorrelation sequence used in MFCC, LPCC, PLPCC, etc.. instead of the cepstrum?


Same reason, because we need to remove multiplicative effect of slowly varying component and fast varying component.

In speech signal processing slow varying component represents different phonemes and thus act as feature vectors for many applications(ex ASR). hence we need to remove the effect of fast varying component to isolate slow varying component.