It is necessary to give up ahimsa, non-harm, if one is to practice compassion. It is necessary too to give up sympathy to practice compassion.
Consider, when a lion hunts, captures, kills and eats a sheep, it is as wrong for you to feel the pain of the sheep as it is to feel the joy of the lion. Indeed, both views are limited. Sympathy is limited. Did it not occur to you that the lion is defending the plants from the sheep: where is your sympathy for these beings? Some would, out of sympathy, refrain from building a house without harming the earthworms displaced by the foundation - what of all those beings which rely on the grasses and trees displaced by the house? What of their shelter, their home, their food? The lion harms the sheep, it is true, but this blood spilt is a righteous sacrifice. The sheep, without the lions, would cause regrettable harm.
The lion, the sheep, the grass - each are closely related. When it is understood that a human and an earthworm share more than half their genetic material, and descended from a common ancestor, each requiring the same amino acids to survive, each eating of the same vegetable matter, sharing the same home and world, it is possible to understand the common ancestry each shares with the plants they require for food, and the lion which protects these plants from the sheep. It is possible to see the brotherhood shared with worm, lion, sheep and plant, to see the brotherhood shared with all other people. We are all the same expression of life.
And it is possible, upon understanding the generations of your family, stretching through the eons, to the lion, the sheep, the worm, the plant, even the bacteria in your wounds, to understand then the nobility of all living creatures, and the essential importance of every individual. As each type of being has perfected its existence to a way of life, a niche, each individual by the facts of its survival proves that it is good enough for the challenges of its specific duty in this world. You, too, are uniquely suited to a place and time. Do you not yet know your duty?
It is not by birth that one is ennobled, becoming the envy of Indra and Brahma. It is by self-control that one betters oneself. It is by sacrificing this self, by the ritual of self-sacrifice in your Ashrama, that you can achieve the full promise of your humanity - and come to cultivate true compassion, even for sheep.