In short:
The fact that there is an alternate route from A to B that does not require squeezing does not prevent you from choosing to take a different legal route that DOES require squeezing.
(Still a bit convoluted, but as simple as the question can be answered I believe...)
What a character can't do is move into a space that doesn't require squeezing in a squeezed state. That's tough to visualize:
Code:
AA
AA
█ █
█ CD
█ CD
█ █
BB
BB
If a large character starts at A, heading for B and moves straight down he would not be able to squeeze such that it would only occupy C and the wall squares to the left. Squeezing requires obstacles on BOTH sides and no other alternate move that prevents the necessity to be squeezed. So the character would need to move into the full size CD space even if it planned to continue moving down after that. And if non-beveled corners are preventing diagonal moves then the character is going to have to shift to the right once so that it occupies the BC space correctly when the opportunity presents.
And then the original question is answered in the diagram as well. The character is not required to take the longer route around the pillars to the right instead of squeezing through them.