Why are most humans right-handed? Why are we handed at all, instead of ambidextrous?
Well I’d give my left arm to be ambidextrous 
A quick trip to Ask.com brings up a bunch of stuff.
http://www.ask.com/web?q=why+are+humans+right+handed&qsrc=0&o=0
The explanation I’ve usually heard goes something like this. People devote a huge amount of their motor skills to their hands. With rare exceptions, people can’t perform intricate motor tasks like, say, writing, or sewing, or anything else requiring comparable precision, with any other part of their bodies. The amount of brainpower devoted just to operating our hands is enormous; the brain tissue required to give our hands the ability to manipulate small objects is already disproportionately high. To allow both hands to operate with the dexterity of a person’s dominant hand would increase that demand further. If, instead, our current ability was split evenly between the two hands, neither one would be quite as able to perform fine motor tasks as the dominant hand is now. So the relationship between them is a balance between having both hands useful and also having the ability to perform the most intricate, difficult motor tasks. Allocating more ability to one hand is apparently a net win - both hands are fairly specialized for fine motor tasks, but one moreso than the other, allowing us better ability to thread needles and so on than if that ability was divided evenly between the two hands.
My Developmental Psych prof claimed most folks are right-handed b/c because of their position in the womb while waiting to be born. He said the fetal positioning typically allows for the right arm to have much more movement relative to the left; hence one is born already accustomed to using the right arm/hand. Those of us (like myself and Cecil) who are leftys, he postulated, spend our womb-time in a different position.
Heck if I know - I have no cite other than my recollection of that particular lecture. The most notable thing about this professor was his stunningly attractive daughter (a member of the volleyball squad) and his hesitance to assign too much reading material to our class of approximately 300 students. But it made sense at the time.
If that were the case, nobody would be able to play musical instruments that require a great deal of dexterity with each hand. Especially a string instrument, with which each hand is performing very different - but equally difficult - types of movement, simultaneously.
Um, why not?
I’m sorry, but the only way I can make sense of this statement is if you’re claiming that everyone really is ambidextrous, all appearance to the contrary. I simply can’t figure out what you could possibly be claiming otherwise.