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.
When one gains insight into how reality functions, i.e. the 3 signs of existence and one experiences how mental and physical phenomena are unsatisfactory and suffering then one gains a great deal of compassion for other beings. 

One realizes that all other beings in conditioned existence is "suffering" from the same illness and that the Buddhas medicine can be applied for everyone to gain emancipation.

When one experiences that reality is oppressive and concealed Dukkha and one sees other beings who has not gotten these insights, then great and deep compassion arises because one understands that everyone is in the same boat. Especially when seeing other beings trying to achieve happiness by clinging to phenomena that will slip away and become dukkha a profound level of compassion arises.