Compassion - a trait of what?

You know how Christianity, Islam, Buddhism, Taoism, Stoicism etc... very often underline compassion?

Even some of those who have seemingly reached a new level of awareness and wisdom, often emphasize compassion.
For example, here's a Shaolin monk Shi Heng Yi talking about it:

Shi Heng Yi wrote:

Sometimes external people are overwhelmed with their own life, which is why not always is in their own control... and this is why sometimes people talk things that they don't mean like that, and why sometimes people do things without knowing the consequences of it...
And so instead of blaming them also for it, it can help if you just understand and try to project it at least as good as you can towards them so that you feel compassion for them... because he or she is the same like you. The situation is just different. The circumstances are just different."

Now obviously he makes the false assumption that everyone is essentially the same.
But how can it be? How is it that a person who is into "expanding his consciousness" or whatever... meditates decades on human condition and all they come up is: "Be compassionate. We are all the same. The situations are just different."

I once had a chat with a leftist liberal, blue-haired woman. I said to her that I wonder why rape, beating, shaming for being a slut or disloyal, or other forms of mistreatement never happen to the so-called good women (I mean, relatively good women). I even gave a few examples of this kind of women since her and I do know some of the same people.
I mean there are women who are careful if they need to move at night and they face a bunch of negroes. There are women who will take a detour, when they see this group of negroes approaching from distant. Also, there are women who don't drink themselves at the level of unconsciousness and then get raped. In fact, there are women who don't drink at all.

So this woman I had this conversation with, was obviously very angry; if the gaze could kill... she had that gaze. And she foamed at me, saying "if you understood better the conditions of some poor individuals, you wouldn't be so resentful in your attitudes".

Sure, I understand that some individuals are more hedonistic, animalistic, less conscious of their actions. Does that "understanding" somehow develop sympathy? Should it?

Is this compassion everyone is so fuzzy about, really a trait of high level of intelligence and wisdom, as is promoted in many, if not most world-views?

Does this including-all-and-everyone type of compassion require a false premise and view of "everyone is essentially the same"? Because otherwise I don't see this compassion thing as very rational.

Moderns associate empathy (objective understanding of another) with sympathy (subjective understanding of another)....and if you are not automatically sympathetic you are accused of being antipathetic, i.e., ruled by the emotion of hatred.

It could be associated with 'recovering Abrahamics' and how with the demise of Abraham's one-god, the average man sought to replace the concept with a new one: nationalism, or absolute cosmic order.
In my view the idea of an all-encomassing, all-incusive, omnipotent, omniscient one-god was replaced with the concept of humanity.
God = Humanity; humanity = god.

Compassion is god's unifying essence.
To see yourself ni another is to see god there.
Compassion = to share, or participate in another's pathos.
Sympathy = to see yourself in everything.

At the same time discrimination and negation of other is individuation; the root of identity: I am other than.... 
And 'natural selection' implies discrimination, free-will being an expression of individual power, multiplied by self-awarness.
Natural order is based on multiplicities and an emerging consciousness that can discriminate and choose.
Life differs from non-life because it can choose - even a plant chooses - willfulness.
Higher life is distinguished by its ability - freedom of will - to choose between multiple options - perception, discrimination and choice are essential to life, and everything that attempts to reduce this is, essentially, attempting to reduce the higher to a lower state.

*********
Knowing = data storage; interpretation and accumulation (memory) of experiences, information, data...
Life (organisms) can only perceive and appropriate and assimilate order (patterners) - patterns reduced to abstractions: images, concepts, sensations, ideas = noumena.  
Understanding = perception of patterns in sensory patterns - natural laws, species, types, kinds, being an example of how man perceives patterns in patterns, i.e., in matter, energy and all perceptible order, and their interactivities.

Understanding perceives details that differentiate what seems alike for simpler minds.

Differentiating subjectivity from objectivity is a start.
Empathy is to sympathy/antipathy what subjectivity is to objectivity - a third-person perspective among those who are trapped in first or second-person perspectives: detachment of one's perceptions, judgements, from its self-interests, ego, emotions, producing clarity, i.e., higher order of awareness, discrimination, differentiation etc.

First-person perceptives (animals, i.e., no, or minimal self-knowledge) - leads to second-person perspectives (subjectivity, i.e., projection of self-knowledge into otherness) - leading to third-person perspectives (objectivity, i.e., perception of other and self from a god-like perspective).

Part of a warriors/hunters talent is to enter the mind of another so as to predict and pre-empt their actions, movements, choices.....but not become trapped in a sympathy towards them - although antipathy, in this context, is helpful it can also corrupt judgements/evaluations.