That can be a long answer…

Short answer:

With aluminum wheels, they are all hooked, because it is easier to make that way, and along with an inner tube, allows for a good grip on the tire and the use of high pressure.

With carbon – hookless is easier, cheaper, stronger, and can be safer at lower pressures. Putting a hook on a carbon wheel allows the use of higher pressure, but if not made properly, the hook can cut the tire causing a blowout.

Longer answer:

Hookless, like just about everything innovative, comes from mountain biking. You might notice that car and motorcycle tires are hookless. Like them, hookless mountain bike tires rely on the rim bed (not the wheel flange) to hold the tire in place against the wheel flange. Works well with tire pressure that cars and mountain bikes use.

With a carbon rim, It also makes a stronger rim that is (marginally) wider and easier (less expensive) to make. The down side is that most agree it can’t take much more than 60-70psi. This matter is worsened by the lack of standards and difficulty mounting tubeless that cause blow offs (although most of these are in a garage, not the road).

Beaded carbon rims have the advantage of being able to take more pressure when used with tubes. It’s a little more difficult with tubeless in that there is no tube pressing the tire into the bead (this is not necessary with hookless). The big problem comes in that carbon wheels are molded (not extruded like aluminum). Its easiest to have the mold release at the hooks, leading to some sharp flashing which will cut into a tire if not removed properly (and it not always is). Alternatively, the carbon wheel can be machined to give it the hook. This machining process sometimes exposes the ends of the fiber, and that can also cut through a tire. Of course when a tire fails, people usually blame the tire and not the wheel.