Why are people usually right handed?

It is just worth noting that in some combat disciplines (fencing, for example), left-handedness is an advantage. Fighting a cross-handed opponent is very different to a same-handed one. The angles and attacks are not the same as a similar handed opponent.
Right handed fencers train and fight with more right-handers at the lower levels (due to the distribution of handedness). Left handed fencers have to train mostly with right-handers, too. So lefthanders are expected to fight cross-handed, but for many right handers, it is more difficult, due to lack of practice. So lefthanders can beat right handers just due to this inexperience. At higher levels in the sport, the ratio of lefthanders is much higher than in the general population, and the exposure level to cross and straight handedness goes up for both left and right handed participants, so the advantage diminishes.
This occurs in other sports, too. Cricket, boxing, tennis, all confer some advantage to the lefthanded at the lower levels due to the novelty factor, and increase the percentage of left handed players at the top levels.

Not really, it’s center-left. The right lung is bigger than the left lung and has three lobes to the left’s two.

“Human beings have bilateral symmetry” is a gross oversimplification and falls down the wayside as soon as you cut one’s torso open.

Picture a society (say, Sparta or early Rome) where fighting is done in formation and warrior is the most prestigious profession. Someone who always starts walking on the wrong foot and who has to use weapons with his uncoordinated hand will never do as well as his mates for whom that’s the good hand.

I’m lefty-forced-righty: I can’t draw or write with my left hand, but if you put a tennis racket in my right hand and throw a ball at me, I’ll change hands and hit the ball. Tying the racket to my hand results in not being able to hit anything except the floor when I fall on my ass. Now imagine if instead of a racket it was a sword and I had two guys a yard to the side.

Fascinating. I’m a dude, but I hold babies left handed.
There’s a few tasks I do left handed, like eat, but predominantly right handed.
To me, holding the baby in left leaves right hand free for feeding, adjusting, etc.

I learned to use a computer mouse on either side- I’m ambimoustrous.

But what percentage of humanity has lived in civilizations with formation warfare? It was only developed a few thousand years ago, was never used by most cultures, and died out fairly quickly.

Furthermore, handed-ness doesn’t seem to be strictly genetic, though there may well be a genetic pre-disposition. Some families have more lefties than others, but it’s not like color blindness or something where you can track it.

Nor is handedness something that you can’t unlearn/learn.

If fighting prowess was the filter by which our ancestors all had to pass through, I’m thinking there would be a lot of inheritable traits in our population that we wouldn’t see as frequently as we do. Like myopia, seasonal allergies, or flat feet. I’d also expect to see an uneven distribution of left-handedness, since not every society has had pressure to be militant. I’d also expect males to be less likely, rather than more likely, to be left-handed.

This is a popular, not to mention sensible hypothesis. It may be ties to the unique characteristics of the human brain.

That doesn’t actually explain it. This part is confounding at the moment. There isn’t any real good reason for it. As mentioned above there isn’t a strong correlation between genetics and which handedness among species. Only when humans reached the point of making the sharp sided rock would it make a difference, the pointy stick worked with either hand.

Well, there is no other explanation right now, so it’s as good an answer as any.

Which is what I said. Tool use can’t entirely explain it, because cats (for instance) don’t use tools, but still have a species-wide preference tendency (for the left, as it happens). So there must be something else causing pawedness in cats, and presumably that same mechanism would also be at work in humans, but we don’t know what it is.

I’m not sure if someone mentioned it, but maybe it was due to the Founder effect? (Or is it bottleneck effect, i always confuse them)

For example, if say, all human have a small group of common ancestor of specie X (all the other member of the species perished), and this small group are very much related (a family lets say), and said family is genetically disposed to be right-handed.

It stands to reason that all their descendent would be genetically pre-disposed to right-handiness.