Why does insight lead to to compassion?

Am I correct in asserting that an increasing level of insight into the true nature of things leads to compassion. Or to put it another way insight is a condition for compassion. From my reading it seems that that is true and the more one practices the more one experiences compassion for other beings. Assuming that is true, how does that occur? It has never been obvious to me how insight and compassion are connected. Or am I wrong and they are not connected at all and they are different aspects to the Buddhist path that are developed separately.