Balanced and unbalanced forces
Motion changes only when forces are unbalanced, so equal opposing forces mean steady speed, not necessarily stopping.
A worked example
Forces of 9 N right and 4 N left on the same object give a net force of 9 - 4 = 5 N to the right, and the object speeds up that way.
The mistake people actually make
Balanced does not mean motionless. A skydiver falling at constant speed under an open parachute has air resistance exactly balancing gravity, and is still moving.