I'm not a good Buddhist, so this is what AFAIK. Chance to be reincarnated as human is low, it's rare so we are lucky to be born as one. As human we have a chance to gather good karma and attain enlightenment, thus ending the cycle.

I think rather than punishment, it's more like a lesson. And dukkha is often mistranslated as "suffering", but in reality it's closer to dissatisfaction or unhappiness (sadness) rather than suffering.