According to Newton, if no external net force acting on a system then the system will keep its initial condition whether at rest or moving uniformly in a straight line.
Let's consider a boy riding a bicycle. He exerts a force to the bicycle and the bicycle reacts with the same magnitude but opposite direction to the boy. From an observer outside the system of boy-bicycle, the net external force acting on the system is always zero so there will be no acceleration. However, in our daily life, we have seen that accelerating a bicycle is possible. It seems to me inconsistent, doesn't it?
What is wrong with my argumentation above?