Why at the center of the earth the gravitational force is zero?

if four horses with equal power are pulling one from opposite sides, it will not move. means net force would be zero. same is at center of earth. the mass of earth around center attracts equally to all sides( because geometrical center and center of mass are same). so net force is zero. On the other hand if you think of gravity as a force puling you into the centre of the earth then when you are at the center of the earth gravity must be zeero