Dic: leopard cannot change its spots

Also, the tiger cannot change its stripes.
One can't change one's essential nature.

• He's a conservative, no matter what he says; the leopard cannot change its spots. 

These metaphoric expressions both originated in an ancient Greek proverb that appears in the Bible (Jeremiah 13:23): “Can the Ethiopian change his skin, or the leopard his spots?” It was first recorded in English in 1546.

... The American Heritage® Dictionary of Idioms,

http://www.yourdictionary.com/idioms/leopard-cannot-change-its-spots-a 

Prov. One cannot change the basic way one is.

• Bill may say he'll stop being so jealous after Cindy marries him, but I doubt he will. A leopard can't change his spots.

... http://idioms.thefreedictionary.com/spot