Have 1/2 switched wall outlet. Adding ceiling fan using existing wiring
most direct way to do this would be to add 2 junction boxes in the attic.
the 14-3 from the switch to the outlet cut that with enough length to make it to the ceiling fan.
now you have a wire from the switch to the ceiling fan.
add a 14-2 from the ceiling fan to the rest of the 14-3 that goes to the outlet. add a junction box at that location. connect the red wire to the black ones. white to white. bare to bare.
in the ceiling fan connect the red to the ceiling fan and the black to the 14-2 black. connect all whites together
this way you won't have to cut sheetrock. and you won't have to rewire the devices.
the other way to do this is to fish a new wire from the switch to the ceiling fan recommend 14-3 so you can switch the fan separate from the light.
the only reason i don't recommend this is puling the switch box out of the wall and replacing it can be a pain. but ill walk you threw that if you want.