Although the vast majority have a latin root to their binomial species name, not all do. Latin was the dominant language of academia right up to the 20th Century. Once a convention has been established, it is very difficult to break with tradition. Because Linnaeaus - the father of taxonomy - used latin as his naming language, it just stuck!
However, there are exceptions to this rule.There are animals named after star wars characters (a trilobite called Han solo), there is a small snail from Fiji called Ba Humbugi, a beetle species called Agra vation, and a fly called Pieza Cake. Sort of lets you into a Taxonomists sense of humour!