This probably because Water, Fire and Grass are one of the most important elements of the earth.
They are also the primordial elements. This can easily be linked to the fact that the starter Pokemon are the first Pokemon you actually encounter and have.
These 3 types are also the easiest to pick when teaching someone Pokemon which is often assumed. For this same reason the Trainer School will always tell you that Grass is weak to Fire but strong to water. Water is strong against to Fire but weak to Grass and Fire is weak to Water but strong to Grass. This is because they are very well known cycling types that form a perfect circle.
If the starters were to be steel, psychic and electric then it would be harder for newer Pokemon trainers to get the basics of Pokemon as they would have to learn that Steel is weak to Fire and Fighting whiles they probably don't even know those types yet. This is just a mare example though.
Since a lot of people start playing Pokemon for the first time appear every year, it is assumed that Game Freak just kept this pattern as it is the easiest pattern to follow :)