Even though you can make a ''team'' of three Pokemon, you only battle with the one you select.
So if you have Pokemon A, B and C, and you select Pokemon A, then Pokemon A will go into a 1v1 battle against whatever the opponent picked out of his/her three.
So basically, the system allows you to choose out of three Pokemon to make 1v1 a little more interesting as it requires some prediction and thought to which Pokemon is best suited to send out.