I´ll try to highlight some aspects, but for shure there is lots more to know...
Main load on a fuselage is the circumferal tension stress in the skin due to pressurisation. Therefor preferred orientation of the fibres is in this circumferal direction. If the composite fuselage shall be cheaper and lighter than the conventional aluminum design, you have to avoid any joints in this load direction, so you have to produce seamless tube sections, so to speak.
Unfortunately your outer surface is the one which have to be smooth and tight toleranced, so you have to produce it in a closed female mold. This raises a problem, because automatically winding fibres inside a circular mold is nearly impossible, any tension on the fibres needed to lay them straigt will lift it up from the mold again. And curing under pressure will not work, because it will not push the fibres onto the mold surface, but just tension it. Therefor fuselages like for the raytheon Premier I are wound around a male mold. This makes getting the fuselage from the mold a real hard job, because it is not so easy to split the mold and remove the part. And you have to account for local reeinforcements, which means more wallthickness, or (because of the smooth outer contour) a slightly smaller mold in this area. But fibre tension during layup will be less at these locations, so you may have build in voids or delaminations.
You can design and build excellent composite fuselages, using complicated layup, mix of different materials (pure fibres, unidirectional tapes, fabric of different styles like plain wave, satin etc, non crimped fabrics and many more) will allow you to place fibres in exactly the right orientation and wallthickness you need. This makes your fuselage an excellent lightwight design, and stronger and much more fatigue resistant than metal design. But you have to produce such design by handlayup with skilled people in sophisticated molds. This is the way gliders are produced. You will never build such a design at costs, that can compete with metal. And costs are the driving factor, the operators want to earn money with their fleet, they don´t care about having the most sophisticated, lightwight structure, it must do the job required at a competitative price, and composite is today far from this point.
While producing large continous structures (i.e. wing upper surface), composites are hard to beat. But when it comes to cutouts for doors, windows, manholes, systems etc. your design and the manufacturing process gets horribly complicated. It is of course much easier to mill a door frame from an aluminum block, than placing hundreds of different prepreg pieces in a complicated mold. If time and money plays no roll, you can produce integral door frames in one shot with the outer skin, reducing weight dramatically. But noone will ever pay for this.
The last aspect is repairability. If you damage a door frame on a metal fuselage, you cut out the damaged parts and rivet in some spare parts or add some doublers. This work is done fast, easy and cheap. If it comes to composite repair, it takes time, skilled personal and lots of money. This does include detection of the damage and its extent. You can design composite parts in a way, that cutting out the damaged part and riveting a doubler onto it is possible, but then you can´t optimize your fible placement, you have to build in additional fibres in unloaded directions, just to give the material enough strength for allowing riveted repair. But then your weight becomes equal to metal.
Maybe the higher costs of optimized design will someday succeed, because you get an airframe with no corrosion and fatigue problems, and a virtually unlimited service life. But you have to earn your money now, you won´t buy an expensive plane that eventually saves you lots of money in 20 or 30 years. The airlines have to survive the next few years, and even this seems to be a hard job. Noone can afford to think and invest in such a long term.