This is a great question and one that is important. Let me offer three reasons. First, we should be compassionate to all people. So, by this principle alone we should be compassionate to children. Second, children are delicate. They are still growing and learning. We can shape them in these formative years. So, if we want a culture were children are compassionate adults, most likely they will have to be shown compassion when they are younger. Keep in mind that children are sponges and learn from experiences. So, there is an educational component.
Finally, in a broken world where all people mess up, including children, everyone needs compassion. To extend it is to acknowledge that you need compassion as well.