Some great stuff has been said.
On one level it's a matter of semantics - namely with sympathy and pity, and empathy and compassion, as one can define them distinctly, or lump them together, applying different meanings to such terms. I tend to view sympathy and pity as the same thing; empathy as another, and compassion as yet another thing. I'll pull a lazy and chuck in an expanded/edited post from months back.
To be sympathetic: Is to feel sympathy (pity/sorry) for someone. It's a feeling arising from recognising the hardship/plight of someone.
To be empathetic: Is to feel the other persons feelings and/or is the act of rationally putting oneself in the shoes of another. Empathy builds on top of sympathy and is deeper.
To be compassionate: Is not a feeling, but a moral quality that involves an intention to sincerely help another, and is realised by the acting out of this intention if possible.
Sympathy and empathy in this view belong to the realm of emotion and intellect; whilst compassion to the realm of volition and behaviour (whilst also likely including an emotional and intellectual component). Compassion is thus the realm of choice and action, whilst sympathy and empathy are simply emotional responses distinct from compassion, and either accompanying it, preceding it, or apart from it - depending on how one choose to act based on these feelings. The feelings of sympathy, but especially empathy can help one to be compassionate. Yet feelings of sympathy and empathy, and the ability of being sympathetic and empathetic, by no means make one a 'good person'. For one can feel another persons feelings, but not want to feel them, nor want to help the person whose feelings they're feeling.
In my personal view I think popular thought confuses empathy and the ability to empathise with compassion. The former which doesn't necessary make one a nice and kind person, but the latter (compassion) which does. Just as having $100 doesn't even define a moral quality about a person, but if one was to choose to give it away to a friend in need, then this $100 (like empathy) becomes a tool for being compassionate/kind.
Thus from my end discussing how one has the ability to emphasise doesn't equate with 'being good', 'better' or 'special' - simply that being more empathetic can more readily dispose one to 'be good' or 'act good' in compassion. Maybe sympathy and empathy can be overused and abused - or rather, the capacity to feel in such a manner is depleted despite a willingness to feel them. Yet compassion - the choice to love, and care, no matter how one feels on some level - I don't think that should ever be negated. It's true, emotional distancing, resisting being abused, and saying no has it's place and is necessary, but I don't think compassion has to ever be cast away even in these circumstances. It's a choice to understand, not to judge or condemn, to forgive, and to care for another's well being, no matter what one feels - from anger, indifference, to elation. Eventually the emotions catch up to our choices - well, usually, at least to some degree.