The red lines really are parallel in this optical illusion.
Explanation
This optical illusion is a version of the well researched Zöllner's illusion of direction. We don't have a definitive explanation for this. However, we believe it can simply be stated as an error in the eye's ability to make sense of the illustration as it projects it into a three dimensional space. Furthermore, it can be stated that the mind expects most intersections to occur at close to a 90 degree angle and will "shift" the illustration to make that appear.