If the Big Bang started in a state of low entropy then shouldn't the Big Crunch be in a state of low entropy also? I recently read that:

What our current level of thermodynamics does tell us though is that if there is such a thing as a Big Crunch, the universe will look a lot different as it heads towards collapse than it did when expanding – the universe started in a state of low entropy and high order and will end in a state of high entropy and
  low order.

But shouldn't the order be in a high state and hence entropy becomes a low state in the Big Crunch (assuming a closed universe)?
The reason I write this is because the gravitational forces in a closed universe are so strong they will cause gravitational collapse so the universe will shrink and go backwards, eventually through all the stages of the big bang and become a singularity once more. 
It was my understanding that a singularity has a state of high order and low entropy. Have I got this the wrong way round? 
If so; Can someone please explain why?
 A: Exactly at a singularity, the physics is by definition not well-defined and we cannot assign it a definite entropy.  However, we can discuss the region very close to a singularity (i.e. just after the Big Bang or just before the Big Crunch).  A priori, this region can have either high or low entropy - there's no rule saying that things always have to have low entropy near a singularity.  Indeed, we believe that just after the Big Bang, the universe had very low entropy, while just before the Big Crunch it would have very high entropy - just as your source says.
(You may be thinking that the entropy must be low after the Big Bang because everything is "near the same place."  But this is wrong because (a) that's only taking into account the positional entropy, not the entropy of momenta, and (b) neither the Big Bang nor the Big Crunch did/will occur at any one particular location in space.)
The reason that the universe would have very high entropy just before the Big Crunch is just plain old thermodynamics - in an ergodic system, high entropy states are overwhelmingly more likely than low-entropy ones just by a basic counting argument.  The reason why the universe had very low entropy right after the Big Bang is much less well-understood, although cosmic inflation may have played a role.  The only thing we know for sure is that the universe couldn't have been anywhere close to maximally entropic right after the Big Bang, or we wouldn't be here having this discussion!  (Well, the Boltzmann brain supporters think that we aren't having this discussion, and I'm just a momentary figment of your imagination.  But trust me, I'm real.  Would I lie to you?)
