People who are left-handed are more dextrous with their left hand than with their right hand: they will probably also use their left hand for tasks such as personal care, cooking, and so on. Writing is not as good an indicator of handedness as it might seem, because many people who write with their right hand use their left for everything else.
Generally, males are three times more likely to be left-handed than females. Statistically, one twin of a pair has a 20% chance to be left-handed. Gay people may be up to 39% as likely to be left-handed as straight people (Habib, 2000).
The heart is not that far off center. While it is on the left side of the body, it is still fairly central in location. Protecting it with a shield would only result in a weak selective pressure, and there have not been enough generations since the bronze age.
It predicts that more men would be right-handed than women. However, data indicates that more males are left-handed than females.
Analysis of ancient cave paintings indicate that humanity was right-handed long before the bronze age.
Throughout history and throughout the world, the level of medicine and technology to assist with childbirth has improved. In spite of that, the proportion of left-handed people has not decreased. (In a sense, it has increased because more people see left-handedness as the benign trait it is.)
It does not explain why humans are right-handed by default, with only birth stress making them left-handed. It could, however, explain left-handedness in combination with some of the other theories presented here.
Until very recently in Taiwan, left-handed people were strongly encouraged to switch to being right-handed (or at least, switch to writing with the right hand). It is more difficult to write legible Chinese characters with the left hand than it is to write Latin letters. Remember that "easy" and "difficult" depend on the person using those terms, so your writing may be neater. Because it is supposedly easier to write when moving your hand towards its side of the body, it is easier to write the Roman alphabet with your right hand than with your left. Conversly, Arabic and Hebrew, which go from right to left, would be easier to write with the left hand. Again, "easier" and "harder" are subjective.
It is possible that sun worship relates to the association of the left with evil. People in the northern hemisphere, looking south, would see the sun rise on their left, move rightwards across the sky, and set on their right. In the southern hemisphere the opposite happens. Among cultures from the southern hemisphere, right-handedness is still dominant. No study on left-side connotations from those cultures has been done.
However, since most sun-worshipping cultures see the setting sun as it dying or vanishing, the right side would indicate the negative associations associated with a setting sun. This is the opposite trend from that