I've been trying to find an answer to this question for years and now that you've raised it I'll list some of the thoughts that came to me.
Spiritual teachings say, "we're spiritual beings in physical bodies" this being said it would appear we operate in a mode of learned response and instinctual/visceral response.
The instinctua/visceral coming from a place of non-reasoning, a place of gnosis where we just know (without thinking) something is or is not the thing to do; this place I'd define as our spiritual center, that place from which we receive a sense of right-action and of compassion; insensitivity coming from questioning this compassion in the context of our learned behavior and our ego.
Spirit is, I would say,99% of who we are yet that 1% of physicality is who the majority say we are as shown by our measure of reality: that which is seen. Our phrase "seeing is believing" attests to this. Spirt is boundless and limitless without form, it is the unseen force, that stuff in which we mill around and interact; it's the life force. Spirituality is a belief in this life force; It is not religion, though religion if approached rightly, is a stepping stone. Spirituality is often referred to as metaphysical, a transcendental awareness.
Having listened and read that most of us do not acknowledge spirituality, the idea of morality, though very humane, seems to be a response to fear. Having observed some causes and effects we have a fear of painful consequences, thus "do unto others as you would to you". Morality is a response to free-will, everyone assuming freedom is absolute, their way is the right way-it's attempt at order yet though it speaks humanely, seems a concession to our lack of understanding of the unseen.