Well I heard Chiron was a beautiful cenataur man, whom was hunted and not killed. He had an arrow shot in his side, an arrow that no matter how hard he tried he couldn't pull out. He was in immense pain from his injury, and realized the only way to relieve his pain was to help and cure others in a serious amount of pain (like you say he was skilled in medicine). So our chiron signs represent where we feel the most pain, but productively use our compassion to know what it's like to feel pain to heal others. It's a very religious sign to me because when you think about it the cross and Jesus Christ kinda represent the same thing.