If the ground is what we are, and the self is what looks, then the veil is the question every seeker eventually has to ask: what is in the way? Why, if the Kingdom is already within, do I not see it?
The contemplatives are almost unanimous on the answer. The veil is the seeker. The grasping, the asking, the the-Kingdom-must-be-somewhere-else, the small self running its programs, that is what blocks the view. The Pharisees ask Jesus when the Kingdom comes, and Jesus answers that the asking is the obstacle. The Sufi al-Hallaj says: between me and Thee there is only me.
This is uncomfortable because it relocates the problem from out there, where it could be fixed by getting the right doctrine, the right teacher, the right practice, to in here, where it requires the small self to give way. And the small self has, understandably, no enthusiasm for the operation.
Every tradition’s practical core is, at some level, a method for thinning the veil. The Tao Te Ching’s not-grasping. The Beatitudes’ poor in spirit. Zazen. Dhikr. Lectio divina. The veil does not get removed; it gets recognized, and in the recognition becomes transparent.