I was once told that I must really enjoy the creative freedom to express myself that came with being a graphic designer. This annoyed me because I was being confused with being a fine artist - again. Stated in the simplest of terms the job of a graphic designer is to express a client's message via a medium so that it is understood by a target audience. There is no consideration of whether or not designer self-expression occurs.
Designers need different skills for each part of the message-medium-audience model. These skills go beyond the visual and computer skills traditionally associated with designers.
A graphic designer must understand the message completely but clients often cannot fully express the message. A message contains both an informative/explicit component (e.g. 10% discount today only) and an implicit/emotive component (e.g. amazement, reliability). While clients are generally good at the explicit message they may need help in deciding on the emotive message. Ask the client for keywords to describe how they want the audience to feel as audience experiences the work. The designer can propose their best initial guess as a starting point for collaboration with the client.
Once the designer understands the message they then use aesthetic ability, technical skill and knowledge with a medium to produce a design work. A skilled designer will produce work that is sympathetic to the medium so that the message is enhanced by the medium instead of fighting it. For example a web design is going to naturally feel more modern than a newspaper ad.
There is a political dimension to the message-medium-audience model. The client signs the cheques so what they insist goes unless the designer is prepared to fire the client. This means that one important part of being a designer is mediating between what is best for delivering the message to the audience and the client's instructions. For example a client might want a picture of their new cat on their website when the audience might be turned off by cats. Graphic designers who are able to deliver the message successfully to the target audience while keeping the clients happy enough to keep the designer in business will ultimately be the most successful.
The message-medium-audience model is very absolute in ignoring the self-expression of the designer. This means that graphic designers must find job satisfaction in the process of design itself and not necessarily in the outcomes. The outcomes might be totally appropriate in delivering the message to the target audience while not artistically stimulating the designer. Therefore designers that desire artistic outlets for self-expression should take up arts as a hobby.