Well, it is interesting

Neanderthal ancestors were mostly right-handed: Scientists find evidence in an odd place: front teeth

Humanity's right-hand dominance might be more than 500,000 years old, new research indicates. The trait of right-handedness is commonly believed to be a sign of the development of another uniquely human trait — language.

"We are right-handed because the left side of the brain controls the right side of the body, and the left side of brain is where language is processed," study researcher David Frayer, of the University of Kansas, told LiveScience. "This is important because it tells us that they were brain lateralized just like we are, and they probably had a language capacity."

Previous studies of ancient humans have shown evidence of handedness in tools, cave art, and bones, but these types of handedness data have been controversial.