Do you believe in gray areas? Binary logic doesn't do them. Something is either entirely true as defined by the premises, or entirely false as defined by the premises.
Can you
always express a given truth in a binary fashion given sufficient complexity? I don't even know, but if you cant, binary logic simply would not allow things which exceed this to exist.
Consider the continuum fallacy. Or the Sorites paradox.
http://en.wikipedia.org/wiki/Sorites_paradox
How are these things addressed? By MVL, and
Hysteresis among other things. Yes, many of these problems can somehow be handled in binary logic, but complexity increases dramatically for anything non-trivial. There is no 'kinda true' there - all bits in a given problem are either completely true or completely false, without even an 'unknown' anywhere.