Back in the old days, the ability to compose with pencil and paper was a given, as that was the only way to get the job done. Today many composers especially those born before 1940, still compose in this way, and in fact prefer to do so despite the great advances of modern technology. For many this is their ideal way to compose music. Why would someone forego the tools of the 21st century for the primitive pencil and paper methodology?
Often times a piece of music will be heard internally in one's head. To sit down at an instrument such as a guitar or piano will only serve to distract the composer from what they are hearing inside. The ability to concentrate on the vision without getting sidetracked is the primary advantage to composing with pencil and paper. It allows one to remain in a meditative space and concentrate on listening intently and then capturing what one hears. Pencil and paper based composition has no inherent sound feedback so the skill is to write the music as it comes without getting sidetracked on the sound. Often when playing a melody on a piano or keyboards, the sound will distract the composer to where they lose sight of the overall piece.
On the other side of the coin, to compose with pencil and paper in conjunction with an instrument of choice, such as a guitar or piano, can be a great productive strategy. Pencil and paper can travel anywhere, though with the advent of small computers that is becoming somewhat of a mute point. Many prefer to bring manuscript and pencil and sit at a piano having been taught the skill in music theory and composition classes in school.
The greatest barrier for most to be able to quickly compose with paper and pencil though, is the ability to hear the music in one's head, and quickly and fluidly translate those tones into notes on paper. In music schooling this was a required skill for composers, but is often neglected in modern times. Many cannot write down that which they hear in their head, and would take a long time to scratch it out on paper. This applies especially to those who are growing up with 21st century tech, whereby immediate auditory feedback is offered as one “pen's” each note into a computer.
Modern technology has taken the pencil and paper process and captured it on the screen. Modern manuscript software is really coming of age, and can't be beat as far as the finished product of a produced score is concerned. Scoring software also has the advantage of being able to hear the product somewhat as it is being worked on, which is a necessity for many. The feedback afforded with modern software is indeed a wonderful tool.
Is composing with pencil and paper for every musician? Perhaps not, and it seems to be a dyeing skill in the computer age. Many have grown up with this skill and feel most comfortable using it. It does take a certain rare ability to be able to hear music and quickly translate it into written tones, a skill that many modern composers do not possess. If it feels right for you, by all means, pursue it. You will need to train yourself in the art of translating tone into pencil strokes fluidly. If it feels too difficult, skip the traditional route and follow your instincts and find what works for you as you develop your own particular methodology.