In his book, he noted, “I have prayed for years for one good humiliation a day, and then I must watch my reaction to it. In my position, I have no other way of spotting both my well-denied shadow self and my idealized persona.”
Rohr is very attuned to the presence of the ego in all spiritually-inclined people and is forthright about wrestling with his own ego daily. I think that his daily prayer for “one good humiliation a day” is his way of asking for his eyes to be opened daily to his own frailty and egotism. For, it is often very humiliating when this happens to someone, especially one who holds himself/herself forth as a “spiritual person.”
I do not think he is calling for us to deliberately go out and humiliate ourselves each day. He is merely asking us to pay attention, to be honest with ourselves, to practice “mindfulness” and be prepared to embrace the subjective experience of a sudden illumination about our own “flesh” being hard at work in our spiritual practice.