That's one thing I've wondered about for as long as I have ridden.
I don't know. Deep down, I feel it sometimes has to do with dominance, but I like to see it as a kind of connection, a connection that attempts to equalize the power dynamics between horse and rider. After all, the horse is, for the most part, submitting to the will of the rider. What can the horse really do to bend the rider to its will?
Allowing the horse to initiate bodily contact for a while is but a small token. I'm happy to be your grooming partner/scratching post for the minute.
Of course, I have had a few horses nudge too hard, but I always push back, and being aware of body language, I pet it accordingly. This ensures that the interaction is mutual and reciprocal, and you're not just a push-over.
Speaking of pushing, I actually invented an exercise designed to make people more confident with horses. It's just a shame it isn't adopted by any formal trainer.
Stand beside the horse. With control of the horse's head, slowly and firmly push the horse sideways across the yard. Horse, like humans, do wonder what you are doing. Depending on your strength of will, the horse can be trained to be totally obedient.
Speaking from a decade of basic experience, I guess interacting with animals is all about a sense - a primitive, basic feeling. After all, they cannot talk to us and tell us in words how they feel. I can only know what I feel about the situation, without clarification. And yet, I have a silent expectation that they would do so. Maybe I'm treating them too much like humans. Maybe I see things this way because I am somewhat egalitarian at heart. I treat people like people indiscriminately. I want others to treat me the best they can, too.
So, I'll ignore this part of animal nature and transcend this dominance, pecking-order hierarchy when I'm riding, as I do in every other area of life.