"No one is born hating..." vs. "No one is born to hate..."

“No one is born hating another person because of the color of his skin, or his background, or his religion. People must learn to hate, and if they can learn to hate, they can be taught to love, for love comes more naturally to the human heart than its opposite.”

Source: Nelson Mandela, Long Walk to Freedom

Why can't it be "No one is born to hate another…"?

There's nothing stopping it from being as you write, but the words were chosen by Nelson Mandela to evoke a certain meaning. Here, he evokes a state of being. A newborn acting as soon as it is born. Had he chosen "to hate", then there is less finality to the statement.

Consider:

This baby was born to hate.
This baby will hate at some point in the future.

vs

This baby was born hating.
This baby is actively hating from the moment of birth.