It's an oft asked question. It has many answers. Firstly, lethality. The Hackbutts and Gonnes of the 15th and 16th C carried muzzle energy of over a thousand foot pound. A 140lb draw weight English yew longbow about 200 at range. Next. Simplicity. Now this sounds mad. A arquebus has the steps ground your piece, draw your flask, pour your powder, replace your flask, draw your ball, place your ball, draw your rod, ram your ball, replace your rod, port your price, draw your flask, open your pan, prime your pan, replace the flask, gaurd your powder, cock your your piece, blow your match, shoulder your piece, present, give fire.

So how the mark dickens is that simpler than the bow? Bow steps: draw your arrow, nock your arrow, bend your bow, give fire.

Very simple answer. A bowman would need to be exercised each week at the butt's on the village green to build and maintain the strength to fire a longbow. From the age of about eight this was part of life and the population would practice by law after the age of 14.

A musket could be put in the hands of an idiot and in six weeks they would be drilled. Better that than ten years of training. Longbowmen , by excavation of battlefields, had huge chests, strong right arms and a bend to their spines.

Next. Fear. The report of a gonne would cause horses to buck and flee. As musketeers became more commonplace, cavalry were trained to be accustomed to gunfire, but by then the musket was dominant.

Next. Its a new toy. I mean, come on. It has fire, smoke and moving parts, it really is the future. Buy yours now or be left behind.

Next. Armour. As evidenced by modern tests, a hardened bodkin arrow head would punch through well made plate at... Oh, hang on... It doesn't. Bows bounce off steel. True today as always. So how did us Britons win at Agincourt and Crecy? We fired tens of thousands of arrows that killed horses and attrition took its toll. Muskets almost ignored the finest plate. Each hit was a man out of action.

Next. Development. The longbow for a long while stalled. It today has pulls gears, carbon fiber composite plastics and red dot sights. That's all from the 1980s. Guns developed apace. Firelock, matchlock, snaphaunce, flintlock percussion lock, bolt, caseless. Muzzle loading, breech loading. Single shot, repeater, semi automatic, automatic. Caliber, ammunition, operating system. The scope for development outpaced the stick with a string.

Hope this helps. There is many more reasons. Almost too many to mention.