John Stevens Sensei, my current sensei and current leader of Classical Aikido, says:
Shiho giri is synonymous with shiho hai, "four-direction respect". All of our activities, in and out of the training hall, should begin and end with rei, "respect". Respect originates with gratitude, gratitude for all the things responsible for our existence. "Four" symbolizes the Four Gratitudes: gratitude toward the Universal from which we received our animated spirit; gratitude toward our parents from whom we received our body; gratitude toward nature from which we receive our sustenance; and gratitude toward our fellow beings from whom we receive life's daily necessities. We cannot survive without the assistance of others, and must never cease to be grateful in "all directions".