Maybe because crossing the midline promotes communication between the two hemispheres, allowing the right hemisphere to contribute its way of filtering experience to that of the left hemisphere. Left hemisphere compartmentalises info and in my opinion is primarily for our survival as a physical entity. The right hemisphere on the other hand is intuitive, connected to spirit, and sees the bigger picture therefore left brain is more likely to perceive from a fear-space, and right brain from a space of peaceful all-knowingness. If you are interested I recommend Iain Mcgilchrists book The Master and His Emmisary. Iain is a psychiatrist with a spiritual flavour.