Why are fibrous proteins insoluble in water?
Fibrous proteins are insoluble in water because their surface is primarily comprised of amino acids with non-polar side-chains.
Fibrous proteins do not dissolve in water due to the difference in polarity. According to chemical laws, "like dissolves like". Since water is polar, and the surface of fibrous proteins is covered in non-polar amino acids, it does not dissolve into the aqueous solution.
Explanation of Polarity:
Polarity is the distribution of charges throughout a molecule, with areas of high electron density holding a partial negative charge, and areas with low electron density holding a partial positive one. When a partial positive charge comes into proximity to a partial negative charge, they attract each other (just like magnets with north and south poles, except with charges instead of magnetic fields). This attraction is usually strong enough to dissociate the solute (the object added to the water/solvent) into individual molecules.
Due to a lack of partially charged zones on the surface of fibrous proteins, they are not attracted to the partial charges of the water molecules, and therefore do not dissociate from each other, keeping the mixture of protein and water heterogeneous.