Skeletal muscles work in pair because of the limitation that these muscles can only contract or pull and can only move in one direction. Since the muscles cannot expand or push, another set of muscles are required for motion in the opposite direction. Skeletal muscles, which are a type of striated muscles, have this limitation in motion because they are fixed to the bones by means of tendons.
In other words, skeletal muscles have to work in pair to produce a motion, such as bending a joint, with only one type of muscle in action. Skeletal muscles are pulling or contractor muscles. Both the contractor muscles connected to the joint work in opposite directions to make the motion. Both these muscles will then reverse the direction of their action when straightening the joint. This pair set of muscles are known as flexors and extensors. The flexor muscle helps in movement in the direction of bending a joint, while the extensor muscles helps in movement in the direction of straightening out a joint.
This pairing action of skeletal muscles is precisely this mechanism which helps the movement of the joints, such as straightening or bending an arm, or even fingers. But an effective way of understanding is by following the example of biceps and triceps, the sets of muscles with which even those lacking advanced knowledge of anatomy are familiar.
In the case of arm muscles, the biceps contract when you bend the arm towards your shoulder, while the triceps flex. Conversely, the triceps contract when you are extending your arm, away from your shoulder. This motion is supported by the flexing action of the biceps. So while you are apparently making a single motion, the respective skeletal muscles are moving in two directions to make it possible. By themselves, either biceps or triceps cannot make your arm move in the direction you are willing to move them.
In simple words, without the absence of one of these sets of muscles, your arm would either remain extended or bent permanently.