The nature of compassion isn't coming to terms with your own suffering and applying it to others: It's knowing that other folks around you suffer and, no matter what happens to you, no matter how lucky or unlucky you are, they keep suffering. And if you can do something about that, then you do it, and you do it without whining or waving your own fuckin' cross for the world to see. You do it because it's the right thing to do.
Many animals experience pain, anxiety and suffering, physically and psychologically, when they are held in captivity or subjected to starvation, social isolation, physical restraint, or painful situations from which they cannot escape. Even if it is not the same experience of pain, anxiety, or suffering undergone by humans- or even other animals, including members of the same species- an individual's pain, suffering, and anxiety matter.
Humans who enslave, castrate, experiment on, and fillet other animals have had an understandable penchant for pretending animals do not feel pain. A sharp distinction between humans and 'animals' is essential if we are to bend them to our will, make them work for us, wear them, eat them without any disquieting tinges of guilt or regret. It is unseemly of us, who often behave so unfeelingly toward other animals, to contend that only humans can suffer. The behavior of other animals renders such pretensions specious. They are just too much like us.