You can think of putting the solid rocket propellant inside the casing as a bit like concrete pouring. Similarly to concrete you need some kind of mixer at the factory. If you stop stirring it gets solid quickly. The propellant is poured into the casing and it later solidifies. And just like concrete if you get the formula wrong or it is cured improperly you get cracks in the solidified propellant. Which can cause the rocket to instantly explode in the pad or in flight after you lit it up. Solid rockets typically have no benign failure modes.
Also much like concrete it weighs a ton. A solid rocket of similar performance to a liquid rocket typically has less volume but higher weight. It is just how it is. The Isp, which you can think of as fuel efficiency, of liquid rockets is also typically higher than for solid rockets. You can typically get more range with a liquid rocket of similar mass to a solid one.
The casing of solid rockets in the old days used to be made of pretty heavy gauge steel. But nowadays they use carbon fiber because it makes it lighter. Which increases the rocket range and/or payload.
If you really want to know what the solid fuel is made of. It depends. Some rockets use HTPB (polyurethane) as the binder. Aluminium powder is sometimes used as the fuel, and Ammonium Perchlorate is sometimes used as the oxidizer.