Why does Haiti and Dominican Republic share the same island?

Because they are differente each others. The Dominican Republic got independence of the Haitian Domination in february 27th 1844.

The Haitian are most 86% Black race decendent of the African Slaves and were a Frech Colony. The Dominicans are 76% Mixed race (Spain, African and Tainos) 20% are white (from spain) and the minory 10% are black.