Why can a plane land in zero visibility conditions but not take off in zero visibility?
Using a HUD, an airliner can take off with visibility as low as 300’, and land with visibility as low as 600’. Without a HUD, you need 500’ (and appropriate runway lights/markings, plus regulatory approval) for takeoff, and whatever your autopilot Cat III autoland system (along with the landing runway) is approved to for landing. (Or 1800’ for cases of no Cat II / Cat III capability.) 

As noted, a pure “zero visibility” landing (a Cat IIIc) doesn’t yet exist, because while the autopilot can bring the aircraft to a stop on the runway, some visibility (300’) is still required to taxi clear and get to the parking spot.

Thankfully, visibilities below 500-600’ are pretty rare in most places. Not all airports have the taxiway lighting required for low-visibility (typically, below 1200’ lateral visibility) taxi operations. That is an airport limitation, not an aircraft limit.

Talking about so many feet of lateral visibility, the actual nomenclature is Runway Visual Range, or RVR. That is reported in feet in the U.S., and often in meters elsewhere.