Sometimes I wonder

Sometimes I wonder if left or right hand really means a thing. I mean, with proper training, can't both your hands right equally good? I'm off on an experiment to see if I can get my left hand to learn to write just like my right. With daily exercises I can see my left hand writing getting better, at the moment, it sort of resembles a 9 year old's font. But that's okay! What I am curious to know is that how did we found out what hand we were? Were we taught to be right handed, and some taught left? Or is there something more behind it? My mind seems to be rattled with random questions with no answer.