Suppose i push a box with my hand which has a mass=1kg. I apply a force of 2 newtons and it will accelerate at 2m/s^2. But, according to the third law, the box applies a force on me, which is also equal to 2 newtons, in the opposite direction which will cause ME to accelerate in the backward direction. But this is not the case, i am accelerating forward ( my hand ) but that force ( the reaction of the box ) is forcing me to move backward, and that force is equal to 2 newtons. So i MUST apply a force larger than 2 newtons to move forward, but i am not doing this, i am still applying a force of 2 newtons and accelerating forward.
PS- I know the forces donnot cancel out as they act upon different objects.