Given the prehistoric and biological leanings of this question, I'd head over to r/askanthroplogy instead.

A general right hand preference in the population has been around for a very long time indeed. There has actually a fair share of research on the topic, though a definitive consensus for the reason this preference developed is still missing.

What we do know, is that many animals show random paw preference, and several monkeys and apes show a tendency for right-hand preference. Chimpansees in particular show the highest ratio of right-handed individuals in the population (except for humans), with a 2:1 rato right - left handedness..

Also, archeological/historical evidence shows a clear right-hand preference across all societies at all times in human (pre)history. (apparently even pre-historic tools can be shown to be manly made for righties).

There have been some theories regarding the origin of handedness, usually emphasizing combat or tool use as driving factors in the evolution of a right-handed bias in a population, good example study.

Allthough these models nicely explain things like the observed correlation between right-handedness ratios and voilence in different societies, they fail to take into account that only a relatively small part of the variance in handedness is heritable.

Several other studies have looked at more complex interplays between genetics and environement as interacting causal factors in the development of handedness, but all in all they admittedly only explain a small part of the variance.

So, to summarize, handedness seems to be at least party a biological trait, that has been present in a skewed 9:1 ratio in favor of right handedness for as long as we can tell, but we don't really yet know why.