I think a basic part of it is that there is such an instant feedback loop in aikido practice. There is a tendency in lots of activities to serarate "mind & body" and I think aikido practice eventually wears this out and we realize the unity of the system (both macro and micro).
When we're really "into" the practice, we lose "our self" by blending with the other person. I have felt this in many activities. I have talked to many who do not experience this. Possibly aikido or budo practice helps open this door because of the intensity of our interaction in the practice which forces us "out of ourselves."
Just a "what if" idea.