This is a debatable topic and many are set in their ways however if you do not yet have an opinion then the following article may help you form one!
Usually the biggest issue cyclists have against training the upper body is the fear of putting on extra muscle mass (weight and bulk they don’t need) or the fact that they just enjoy riding and do everything they can to avoid the gym.
The type of rider you are can guide the type of training you do. For example sprinters, climbers and track riders need a lot of upper body strength for leverage when pulling and pushing on the bars. If you are a rider who spends time out of the saddle consider that the movement from seated to standing moves your biomechanical axis from pelvis to shoulders, so an appreciation for upper body strength to support is important.
On longer rides there is a unique stress placed on the muscles of the neck, shoulders and upper back. Strengthening the upper body will make it more resistant to fatigue which is important as an upper body that fatigues will result in poor form and cause a decrease in speed. Less fatigue means less room for biomechanical error which will also aid in the prevention of injury.
Have you ever tried pushing the pedals without holding onto your bars? Apart from losing balance (unless you practice) the core and upper body give a base for your legs to push off ensuring the force is transmitted efficiently with little power loss.
Riders who do not utilize their core and upper body strength properly will likely produce a lot of upper body movement which will result in a loss of power. Next time you are riding with a group see if you can spot this.
Health & Well being
As we know cycling is a non-weight bearing sport where there is a lot of sweating (calcium loss) involved contributing to bone density loss, an issue also associated with aging and menopause in females. Increased muscle mass can prolong the effects as well as decreasing fat and increasing glycogen distribution.
All things considered there is more to cycling than a powerful, toned, shaven lower body and a super conditioned cardio respiratory system. Look to keep variety and total body balance with a well-rounded approach to your training program in relation to the type of cyclist you are.